Inclusion Criteria:

          1. Has histopathologically confirmed locally advanced or metastatic cancer (solid tumor
             or lymphoma) that has progressed following at least 1 line of therapy if a regulatory
             approved or standard of care therapy exists and no other standard therapy with proven
             clinical benefit is available or the patient declines further standard of care.

             Note: Must have measurable disease per RECIST v1.1 or RANO as assessed by the local
             site investigator/radiologist. Lesions in a previously irradiated area are measurable
             if progression has been demonstrated after radiation. Lesions must be measurable in at
             least 2 dimensions in a spiral CT scan or MRI. For lymphoma patients only, the minimum
             measurement must be >15 mm on the long axis and >10 mm on the short axis.

               1. Must provide access to de-identified historical scans or scan reports for the
                  assessment of the patient's rate of progression on and after their previous
                  regimen, if available.

               2. Must provide access to existing formalin-fixed biopsy tissue or slides for
                  histology assessments if a pretreatment biopsy is not performed or unsuccessful
                  for any reason.

          2. In the anti-PD-1/L1 therapy refractory cohorts, patients must have first had a
             clinical benefit from (complete response or partial response of any duration, or
             stable disease for at least 16 weeks) followed by documented disease progression while
             on or following anti-PD-1/L1 treatment (administered either as monotherapy or in
             combination). Patients may not have received intervening cytotoxic chemotherapy
             between finishing anti-PD-1/L1 treatment and commencing study treatment. Progression
             is defined by meeting all of the following criteria:

               1. Has received anti-PD-1/L1 therapy at least twice if dosed every 4 weeks (q4w) or
                  longer, 3 times if dosed every 3 weeks (q3w) or 4 times if dosed every 2 weeks
                  (q2w).

               2. Has demonstrated progressive disease (PD) while on or after anti-PD-1/L1 therapy
                  as defined by RECIST v1.1 or RANO.

                  Note: Patients who have experienced Grade 3 or greater immunological adverse
                  events (irAE) on previous anti-PD-1/L1 therapy before 16 weeks may also be
                  included in monotherapy cohorts regardless of disease response.

          3. Is an adult ≥18 years of age on day of signing informed consent.

          4. Has an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1.

          5. Has an estimated life expectancy of >3 months.

          6. Patients who have surgically accessible lesions must agree to biopsies from
             nonirradiated tumor lesions or irradiated tumor lesions that have shown progression
             since irradiation. If no surgically accessible lesions exist, patients must consent
             for Sponsor to access historical biopsies.

             a. For lymphoma patients only: patients must be able to provide a core or excisional
             lymph node biopsy for biomarker analysis from a newly obtained biopsy prior to drug
             treatment.

          7. Is able to swallow capsules and/or tablets.

          8. Has adequate organ and bone marrow function defined by:

             - Absolute neutrophil count ≥1.5 × 109/L (≥1500/mm3).

               -  Hemoglobin ≥9.0 g/dL or equivalent.

               -  Platelet count ≥75 × 109/L (≥75,000/mm3).

               -  Total bilirubin ≤1.5 × institutional upper limit of normal (ULN), unless known
                  Gilbert syndrome has been diagnosed.

               -  Measured or calculated creatinine clearance (glomerular filtration rate) ≥50
                  mL/min/1.73 m2.

               -  Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤2.5 × ULN or
                  ≤5 × ULN with cancer in the liver.

               -  For cohorts receiving LNS8801/pembrolizumab combination therapy with
                  pembrolizumab, prothrombin time (PT) or activated partial thromboplastin time
                  (aPTT) must be ≤1.5 × ULN. If a participant is receiving anticoagulant therapy,
                  PT or aPTT must be within therapeutic range of intended use of anticoagulants.

          9. Female patients of childbearing potential must have a negative serum pregnancy test at
             screening and a negative (serum or urine) pregnancy test within 72 hours before the
             first dose of study drug. If the urine test is positive or cannot be confirmed
             negative, a serum pregnancy test will be required and must be negative for the patient
             to be eligible.

         10. Female patients must not be breastfeeding.

         11. Female patients of childbearing potential must be willing to use a highly effective
             contraception method before study entry, while on study drug, and for a period of at
             least 4 months after the last dose of study drug.

             Note: Women receiving estrogen-based contraceptives will be excluded from the study.

             Note: A woman is considered of childbearing potential unless she is postmenopausal (≥1
             year without menses and confirmed with a follicle-stimulating hormone test) or
             surgically sterilized via bilateral oophorectomy, hysterectomy, bilateral tubal
             ligation, or successful Essure® placement with a documented confirmation test at least
             3 months after the procedure.

             Male patients must be surgically sterile or willing to use a highly effective
             double-barrier contraception method (eg, male condom with diaphragm or male condom
             with cervical cap) upon study entry, while on study drug, and for a period of at least
             4 months after the last dose of study drug.

             (Highly effective contraception is defined as a method of contraception that has a <1%
             failure rate when used consistently and correctly (as defined by the International
             Council for Harmonization Guidance on Nonclinical Safety Studies for the Conduct of
             Human Clinical Research M3 [R2]). These methods include implants, injectables,
             combined hormonal contraceptives (eg, combined oral contraceptives [excluding
             estrogen-based contraceptives], patch, and vaginal ring), some intrauterine devices
             (IUDs) (eg, IUD or intrauterine system), sexual abstinence, or a monogamous
             relationship with a vasectomized partner. True abstinence, when in line with the
             preferred and usual lifestyle of the patient, is considered a highly effective method
             only if defined as refraining from heterosexual intercourse during the entire period
             of risk associated with the study drug (ie, 60 days after discontinuing study drug or
             5 times the terminal elimination half-life, whichever is longer). Periodic abstinence
             (eg, calendar, ovulation, symptothermal, or post ovulation methods) and withdrawal are
             not acceptable methods of contraception.)

         12. Is able to understand and voluntarily sign a written informed consent form and is
             willing and able to comply with protocol requirements.

        14. Phase 2A cohort-specific inclusion criteria are provided below: Monotherapy (M) cohorts
        will be dosed with LNS8801 alone. Combination (C) cohorts will be dosed with LNS8801 and
        pembrolizumab.

        a. COHORT M1: i. Advanced solid tumor malignancy ii. Received ≤4 prior lines of prior
        systemic therapy. iii. PD-1/L1 refractory as described in inclusion criteria 2, above. iv.
        No available standard of care as described in inclusion criteria 1, above.

        b. COHORT M2: i. Advanced solid tumor malignancy. ii. Received ≤ 2 prior lines of prior
        systemic therapy. iii. No available standard of care as described in inclusion criteria 1,
        above

        c. COHORT M3: i. Advanced cutaneous melanoma ii. Immediate prior line of therapy was a
        PD-1/L1 immune checkpoint inhibitor (IO), alone or in combination, and was discontinued due
        to an immune-related adverse event (irAE).

        iii. No available standard of care as described in inclusion criteria 1, above.

        d. COHORT M4: i. Advanced solid tumor malignancy, except cutaneous melanoma. ii. Immediate
        prior line of therapy was a PD-1/L1 immune checkpoint inhibitor (IO), alone or in
        combination, and was discontinued due to an immune-related adverse event (irAE).

        iii. No available standard of care as described in inclusion criteria 1, above.

        e. COHORT M5: i. Metastatic uveal melanoma. ii. No previous PD-1/L1 therapy. iii. No
        available standard of care as described in inclusion criteria 1, above.

        f. COHORT M6: i. ALK mutation-positive non-small cell lung cancer (NSCLC). ii. No available
        standard of care as described in inclusion criteria 1, above.

        g. COHORT C1: i. Advanced solid tumor malignancy. ii. Received ≤4 prior lines of prior
        systemic therapy. iii. PD-1/L1 refractory as described in inclusion criteria 2, above iv.
        No available standard of care as described in inclusion criteria 1, above.

        h. COHORT C2: i. Advanced solid tumor malignancy. ii. Received ≤2 prior lines of prior
        systemic therapy. iii. No available standard of care as described in inclusion criteria 1,
        above.

        i. COHORT C3: i. Metastatic NSCLC expressing PD-L1 with a Tumor Proportion Score (TPS) ≥1%
        and ≤49% as determined by an FDA-approved test ii. Must not have EGFR or ALK genomic tumor
        aberrations or have demonstrated disease response on or following FDA-approved therapy for
        these aberrations.

        iii. Eligible for pembrolizumab as the standard of care or no available standard of care
        available.

        j. COHORT C4: i. Metastatic or unresectable, recurrent Head and Neck Squamous Cell Cancer
        (HNSCC) expressing PD-L1 with a Combined Positive Score (CPS) ≥1 and ≤19 as determined by
        an FDA-approved test ii. Disease is either treatment-naive or with disease progression on
        or following platinum-containing chemotherapy.

        iii. Eligible for pembrolizumab as the standard of care or no available standard of care
        available.

        k. COHORT C5: i. Metastatic uveal melanoma. ii. No previous PD-1/L1 therapy. iii. No
        available standard of care as described in inclusion criteria 1, above.

        l. COHORT C6: i. Malignant cutaneous melanoma. ii. No available standard of care as
        described in inclusion criteria 1, above

        Exclusion Criteria:

          1. Has thyroid cancer or gall bladder cancer (excluded from Phase 1 cohorts only).

          2. Has any cancer that is known to be estrogen receptor-positive (ERalpha+).

          3. Received an anticancer therapy within 4 weeks (6 weeks for nitrosoureas, mitomycin C,
             or pembrolizumab given on a 6-week cycle) or 5 half-lives, whichever is shorter,
             before the first dose of study drug. Except in anti-PD-1/L1 refractory cohorts, where
             patients may start LNS8801 therapy at what would be the beginning of the next cycle of
             their immunotherapy cycle (eg, LNS8801 may be dosed 3 or 6 weeks after the last dose
             of pembrolizumab depending on cycle, or 4 weeks after nivolumab) if that is shorter.

          4. Has unresolved toxicities from previous anticancer therapy. Anticancer therapy
             toxicities are defined as toxicities (other than alopecia) not yet resolved according
             to the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events
             (CTCAE) v5.0 ≤ Grade 1, or baseline (participants with ≤ Grade 2 neuropathy may be
             eligible).

               -  Note: Patients in an LNS8801/pembrolizumab combination cohort must not have
                  undergone prior allogeneic hematopoietic stem cell transplantation within the
                  last 5 years. (Participants who have had a transplant greater than 5 years ago
                  are eligible as long as there are no symptoms of acute graft versus host disease
                  [GVHD])

          5. Patients must not be participating in another study of an investigational agent or
             have used an investigational device within 4 weeks before the first dose of study
             drug.

             Note: Patients who have entered the follow-up phase of an investigational study may
             participate as long as it has been 4 weeks after the last dose of the previous
             investigational agent.

          6. Has a symptomatic primary central nervous system (CNS) tumor, symptomatic CNS
             metastases, leptomeningeal carcinomatosis, or untreated spinal cord compression.

             Note: Patients are eligible if neurologic symptoms and CNS imaging are stable and
             steroid dose is stable for 14 days prior to the first dose of study drug and no CNS
             surgery or radiation has been performed for 28 days (14 days if stereotactic
             radiosurgery).

             a. In a LNS8801/pembrolizumab combination cohorts, has known active CNS metastases
             and/or carcinomatous meningitis.

          7. Requires the use of antitumor necrosis factor (anti-TNF) therapies, such as
             infliximab, or has received treatment with anti-TNF therapies within 5 half-lives of
             that therapy.

          8. Has an active autoimmune disease that required systemic treatment in the past 2 years
             (ie, with use of disease-modifying antirheumatic agents or immunosuppressive drugs).

             Note: Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid
             replacement therapy for adrenal, thyroid, or pituitary insufficiency) is permitted.

          9. Has a diagnosis of immunodeficiency, is on immunosuppressive therapy, or is receiving
             chronic systemic or enteric steroid therapy (in dosing exceeding 10 mg/day of
             prednisone equivalent) or any other form of immunosuppressive therapy within 7 days
             prior to the first dose of study drug.

             Note: At screening, patients may be using systemic corticosteroids (dose 10 mg/day of
             prednisone or equivalent) or topical or inhaled corticosteroids.

         10. Is receiving any other investigational agent(s) or has received an investigational
             agent within 30 days or 5 half-lives, whichever is shorter, of the first dose of study
             drug.

         11. Has had major surgery (excluding placement of vascular access) within 4 weeks prior to
             the planned start of LNS8801.

         12. Has had radiotherapy with a limited field for palliation (less than 2 weeks) within 1
             week of the first dose of study drug to non-CNS disease, with the exception of
             patients receiving radiation to more than 30% of the bone marrow or with a wide field
             of radiation, which must be completed at least 4 weeks prior to the first dose of
             study drug. Participants must have recovered from all radiation-related toxicities,
             not require corticosteroids, and not have had radiation pneumonitis.

         13. Has evidence of pneumonitis or interstitial lung disease.

             a. For pembrolizumab combination cohorts, has a history of (noninfectious) pneumonitis
             that required steroids or has current pneumonitis

         14. Has any of the following known infections:

               1. Human immunodeficiency virus (HIV), hepatitis B virus (HBV) (ie, hepatitis B
                  surface antigen-positive), or hepatitis C virus (HCV) (ie, detectable HCV
                  ribonucleic acid [RNA]).

                  Note: Patients with a prior history of treated HBV infection who are
                  antigen-negative or patients with a prior history of treated HCV infection who
                  are HCV RNA-undetectable may be enrolled.

               2. Active infections requiring systemic therapy (including asymptomatic infections
                  with positive virus titers and the Investigator's judgment that worsening of the
                  condition is likely with study drug or the condition would impair or prohibit a
                  patient's participation in the study).

         15. Has active malabsorption syndrome or other condition likely to affect gastrointestinal
             absorption of the study drug.

         16. Has received a live vaccine within 30 days of the planned start of study drug.

         17. Has a corrected QT interval (QTc) by Fridericia method >450 msec for male patients or
             >470 msec for female patients, or a history or risk factors for or use of medications
             known to prolong the QTc or that may be associated with torsades de pointes.

             Note: Isolated right bundle branch block and incomplete right bundle branch block and
             left anterior hemiblock are acceptable.

         18. Has had any prior treatment for the present solid malignancy with GPER agonists (eg,
             tamoxifen, raloxifene, or estrogen hormone replacement therapy). History of oral
             contraceptive use is permissible.

         19. Is using a strong inhibitor or inducer of cytochrome P450 1A2, 2C9, 2C19, 2D6, or 3A4.

         20. Requires treatment with a proton pump inhibitor.

         21. Has received estrogen treatment since cancer diagnosis or the presumed initiation of
             their cancer, including estrogen-based contraceptives.

         22. Has a cancer that was treated with estrogen hormone therapy.

         23. Is currently using estrogen hormone replacement therapy, was diagnosed while on
             estrogen hormone replacement therapy, or has used estrogen replacement therapy since
             diagnosis.

         24. Is pregnant, lactating, has been pregnant within the last 2 years, or is planning to
             attempt to become pregnant or impregnate someone during this study or within 90 days
             after dosing of study drug (120 days for LNS8801/pembrolizumab combination cohorts).

         25. Has a history of another active malignancy (a second cancer) within the previous 2
             years except for localized cancers that are not related to the current cancer being
             treated, are considered cured, and, in the opinion of the Investigator, presents a low
             risk of recurrence. These exceptions include, but are not limited to, basal or
             squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the
             prostate, cervix, or breast.

         26. Has an uncontrolled intercurrent illness including, but not limited to, symptomatic
             congestive heart failure, hypertension, unstable angina pectoris, cardiac arrhythmia,
             autoimmune or inflammatory diseases, or psychiatric illness/social situations that
             would limit compliance with study requirements.

         27. Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the study, interfere with the participant's
             participation for the full duration of the study, or is not in the best interest of
             the participant to participate, in the opinion of the treating investigator.

         28. Has a known psychiatric or substance abuse disorder that would interfere with the
             participant's ability to cooperate with the requirements of the study in the medical
             judgement of the investigator.

         29. Has received radiation therapy to the lung that is >30 Gy within 6 months of the first
             dose of trial treatment for patients with non-small cell lung cancer.

         30. In the LNS8801/pembrolizumab combination cohorts, has received prior therapy with an
             anti-PD-1, anti-PD-L1, or anti PD L2 agent or with an agent directed to another
             stimulatory or co-inhibitory T-cell receptor (e.g., CTLA-4, OX 40, CD137), and was
             discontinued from that treatment due to a Grade 3 or higher irAE.

         31. Has had an allogenic tissue/solid organ transplant.