Inclusion Criteria:

          -  Has a histologically or cytologically-documented, advanced (metastatic and/or
             unresectable) solid tumor that is incurable and for which prior standard systemic
             therapy has failed in one of the following cohorts: TNBC, Ovarian Cancer, Gastric
             Cancer, Colorectal Cancer, GBM, BTC (intrahepatic, extrahepatic cholangiocarcinoma and
             gall bladder cancer; excludes Ampulla of Vater), Pancreatic Cancer

          -  Must have progressed on or since the last treatment

          -  Has measurable disease per RECIST 1.1 (RANO for the GBM cohort) as assessed by the
             local site investigator/radiology and confirmed by BICR

          -  Has provided a PD-L1 evaluable archival tumor tissue sample or newly obtained core or
             excisional biopsy of a tumor lesion not previously irradiated

          -  Male participants agree to use approved contraception during the treatment period for
             at least 7 days after the last dose of lenvatinib, or refrain from heterosexual
             intercourse during this period

          -  Female participants are not pregnant or breastfeeding, and are not a woman of
             childbearing potential (WOCBP), OR are a WOCBP that agrees to use contraception during
             the treatment period (or 14 days prior to the initiation of study treatment for oral
             contraception) and for at least 120 days post pembrolizumab, or 30 days post
             lenvatinib, whichever occurs last

          -  Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 within 3
             days of study treatment initiation

          -  Has adequate organ function

        For Triple Negative Breast Cancer Participants:

          -  Has received one or 2 prior lines of therapy

          -  Has Lactate Dehydrogenase (LDH) <2.0 x Upper Limit of Normal (ULN)

          -  Has locally determined results for estrogen receptor, progesterone receptor, and human
             epidermal growth factor receptor 2 tumor analyses

        For Ovarian Cancer Participants:

        - Has primary ovarian cancer and has received 3 prior lines of therapy.

        For Gastric Cancer Participants:

        - Has received 2 prior lines of therapy. Note: Gastric cancer will include participants
        with both gastric and gastroesophageal junction (GEJ) adenocarcinoma. Participants with
        squamous cell carcinoma histology are not eligible

        For Colorectal Cancer Participants:

        - Has received 2 prior lines of therapy

        For GBM Participants:

          -  Has failed initial systemic therapy for newly diagnosed GBM

          -  Have the following time periods elapsed before the projected start of scheduled study
             treatment: 1) at least 3 weeks from prior surgical resection, 2) at least 1 week from
             stereotactic biopsy, 3) at least 6 months from completion of prior radiotherapy, 4) at
             least 4 weeks (or 5 half-lives, whichever is shorter) from any investigational agent,
             5) at least 4 weeks from cytotoxic therapy, 6) at least 6 weeks from antibodies, 7) at
             least 4 weeks (or 5 half-lives, whichever is shorter) from other antitumor therapies
             and 1 week for cancer vaccines

          -  Be neurologically stable (e.g. without a progression of neurologic symptoms or
             requiring escalating doses of systemic steroid therapy within last 2 weeks) and
             clinically stable

          -  Has histologically confirmed World Health Organization (WHO) Grade IV GBM

          -  Has locally determined result for O^6-methylguanine-DNA methyltransferase (MGMT)
             analysis

        For Biliary Tract Cancer Participants:

          -  Has received 1 prior line of therapy

          -  Child-Pugh Score, Class A: well-compensated disease. Child-Pugh Score of 5-6

        For Pancreatic Cancer Participants:

          -  Has pathologically (histologically or cytologically) confirmed pancreatic ductal
             adenocarcinoma that is metastatic at enrollment

          -  Has received one or 2 prior lines of therapy

          -  Has received prior therapy with at least 1 (platinum-containing regimen or
             gemcitabine-containing regimen) but no more than 2 prior systemic therapies for
             unresectable or metastatic pancreatic cancer

        Exclusion Criteria:

          -  Has gastrointestinal malabsorption or any other condition that might affect the
             absorption of lenvatinib

          -  Has present or progressive accumulation of pleural, ascitic, or pericardial fluid
             requiring drainage or diuretic drugs within 2 weeks prior to enrollment (applies to
             all cohorts except the ovarian cancer cohort)

          -  Has radiographic evidence of encasement or invasion of a major blood vessel or of
             intratumoral cavitation. Participants with portal vein invasion (Vp4), inferior vena
             cava, or cardiac involvement based on imaging in the BTC cohort are not eligible for
             enrollment

          -  Has clinical significant hemoptysis or tumor bleeding within 2 weeks prior to the
             first dose of study treatment

          -  Has significant cardiovascular impairment within 12 months of the first dose of study
             treatment, such as history of congestive heart failure greater than New York Heart
             Association (NYHA) Class II, unstable angina, myocardial infarction or cerebrovascular
             accident (CVA), or cardiac arrhythmia associated with hemodynamic instability

          -  Has a history of arterial thromboembolism within 12 months of start of study treatment

          -  Has a known additional malignancy that is progressing or has required active treatment
             within the past 3 years.

          -  Has a serious nonhealing wound, ulcer or bone fracture

          -  Has had major surgery within 3 weeks prior to first dose of study interventions

          -  Has biologic response modifiers therapy (e.g. granulocyte colony-stimulating factor)
             within 4 weeks before study entry

          -  Has preexisting ≥Grade 3 gastrointestinal (GI) or non-gastrointestinal fistula

          -  Has received prior therapy with lenvatinib, 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. cytotoxic T-lymphocyte-associated protein 4 [CTLA-4], Tumor necrosis
             factor receptor superfamily, member 4 [OX 40], tumor necrosis factor receptor
             superfamily member 9 [CD137])

          -  Has received prior systemic anti-cancer therapy including investigational agents
             within 4 weeks prior to study treatment start

          -  If participant received major surgery, they must have recovered adequately from the
             toxicity and/or complications from the intervention prior to starting study treatment

          -  Has received prior radiotherapy within 2 weeks of start of study treatment.
             Participants must have recovered from all radiation-related toxicities, not require
             corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted
             for palliative radiation (≤2 weeks of radiotherapy) to non-central nervous system
             (CNS) disease

          -  Has received a live vaccine within 30 days prior to the first dose of study treatment

          -  Has known intolerance to lenvatinib (and/or any of the excipients)

          -  Is currently participating in or has participated in a study of an investigational
             agent or has used an investigational device within 4 weeks prior to the first dose of
             study treatment

          -  Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy
             (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of
             immunosuppressive therapy within 7 days prior the first dose of study treatment

          -  Has known active CNS metastases and/or carcinomatous meningitis

          -  Has tumors involving the brain stem

          -  Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients

          -  Has an active autoimmune disease that has required systemic treatment in past 2 years

          -  Has a history of (non-infectious) pneumonitis that required steroids or has current
             pneumonitis

          -  Has an active infection requiring systemic therapy

          -  Has a known history of human immunodeficiency virus (HIV) infection

          -  Has a known history of hepatitis B or known active hepatitis C virus infection

          -  Has a known history of active tuberculosis (TB; Bacillus tuberculosis)

          -  Is pregnant or breastfeeding or expecting to conceive or father children within the
             projected duration of the study, starting with the screening visit through 120 days
             after the last dose of study treatment

          -  Has had an allogenic tissue/solid organ transplant (large organ transplants, stem-cell
             transplant requiring chronic immunosuppressant therapy necessary to prevent graft
             rejection)

        For GBM Participants:

          -  Has carcinomatous meningitis

          -  Has recurrent tumor greater than 6 cm in maximum diameter

          -  Has tumor primarily localized to the brainstem or spinal cord

          -  Has presence of multifocal tumor, diffuse leptomeningeal or extracranial disease

          -  Has evidence of intratumoral or peritumoral hemorrhage on baseline magnetic resonance
             imaging (MRI) scan other than those that are grade ≤ 1 and either post-operative or
             stable on at least 2 consecutive MRI scans

          -  Has received Optune® TTFields within 2 weeks of study intervention