Inclusion Criteria:

          -  Participants must have histologically or cytologically confirmed solid malignancy.

          -  Leptomeningeal metastases, as determined by: 1) positive CSF cytology, or 2) MRI
             suggestive of leptomeningeal metastases and atypical cytology.

          -  Age ≥18 years. Because no dosing or adverse event data are currently available on the
             use of pembrolizumab in combination with lenvatinib in participants <18 years of age,
             children are excluded from this study, but will be eligible for future pediatric
             trials.

          -  ECOG performance status ≤ 1 (Karnofsky ≥70%, see Appendix A)

          -  Participants must have normal organ and marrow function; all screening labs should be
             performed within 14 days of treatment initiation.

          -  Eligibility Criteria for Organ and Marrow Function

               -  Hematological

                    -  Absolute neutrophil count (ANC) ≥1500/μL

                    -  Platelets ≥100 000/μL

                    -  Hemoglobin ≥9.0 g/dL or ≥5.6 mmol/La

               -  Renal

                  --- Creatinine ≤1.5 × ULN OR Measured or calculatedb creatinine clearance (GFR
                  can also be used in place of creatinine or CrCl) ≥30 mL/min for participant with
                  creatinine levels >1.5 × institutional ULN

               -  Hepatic

                    -  Total bilirubin ≤1.5 ×ULN OR direct bilirubin ≤ULN for participants with
                       total bilirubin levels >1.5 × ULN

                    -  AST (SGOT) and ALT (SGPT) ≤2.5 × ULN (≤5 × ULN for participants with liver
                       metastases)

               -  Coagulation

                    -  International normalized ratio (INR) OR prothrombin time (PT) Activated
                       partial thromboplastin time (aPTT) ≤1.5 × ULN unless participant is
                       receiving anticoagulant therapy as long as PT or aPTT is within therapeutic
                       range of intended use of anticoagulants

          -  Female participants of childbearing potential should have a negative urine pregnancy
             test within 72 hours prior to receiving the first dose of study medication. If the
             urine test is positive or cannot be confirmed as negative, a serum pregnancy test will
             be required.

          -  A female participant is eligible to participate if she is not pregnant not
             breastfeeding, and at least one of the following conditions applies: Not a woman of
             childbearing potential (WOCBP) OR A WOCBP who agrees to follow the contraceptive
             guidance during the treatment period and for at least 120 days after the last dose of
             study medication

          -  A male participant must agree to use a contraception as detailed in this protocol
             during the treatment period and for at least 120 days after the last dose of study
             treatment and refrain from donating sperm during this period.

          -  If participant is on a daily steroid medication, dose must be stable at ≤2 mg
             dexamethasone (or equivalent) for 7 days prior to initiation of treatment.

          -  Ability to understand and the willingness to sign a written informed consent document.

        Exclusion Criteria:

          -  Participants who have received prior systemic anti-cancer therapy including
             investigational agents within 14 days of protocol treatment. Participants must have
             recovered from all AEs due to previous therapies to ≤Grade 1 or baseline. Participants
             with ≤Grade 2 neuropathy may be eligible.

          -  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-CNS disease.

          -  Participant must have recovered adequately from the toxicity and/or complications from
             any prior surgical procedures prior to starting therapy. Lenvatinib should be held for
             4 weeks following a major surgical procedure, 2 weeks following a minor surgical
             procedure.

          -  Has received a live vaccine within 30 days prior to the first dose of study drug.
             Examples of live vaccines include, but are not limited to, the following: measles,
             mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus
             Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection
             are generally killed virus vaccines and are allowed; however, intranasal influenza
             vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed.

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements.

          -  Has known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirements of the trial.

          -  HIV-positive participants on combination antiretroviral therapy are ineligible because
             of the potential for pharmacokinetic interactions with pembrolizumab. In addition,
             these participants are at increased risk of lethal infections when treated with marrow
             suppressive therapy. Appropriate studies will be undertaken in participants receiving
             combination antiretroviral therapy when indicated. No testing for HIV, Hepatitis B,
             and Hepatitis C is required unless mandated by local health authority.

          -  Participants who are receiving any other investigational agents.

          -  Has a diagnosis of immunodeficiency.

          -  Has a known history of Hepatitis B (defined as Hepatitis B surface antigen [HBsAg]
             reactive) or known active Hepatitis C virus (defined as HCV RNA [qualitative] is
             detected) infection. Note: no testing for Hepatitis B and Hepatitis C is required
             unless mandated by local health authority.

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

          -  Has an active infection requiring systemic therapy.

          -  Has a known additional malignancy that is progressing or requires active treatment
             (except for patients receiving letrozole, anastrozole, exemestane, tamoxifen,
             fulvestrant, trastuzumab, bisphosphonates, denosumab or ovarian suppression therapy).
             Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the
             skin that has undergone potentially curative therapy or in situ cervical cancer.

          -  Has active autoimmune disease that has required systemic treatment in the past 2 years
             (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive
             drugs).Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid
             replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a
             form of system.

          -  Requires treatment with high dose systemic corticosteroids defined as dexamethasone
             >2mg/day or bioequivalent within 7 days of initiating therapy.

          -  Has received systemic immunosuppressive treatments, aside from systemic
             corticosteroids as described in Section 3.2.15, within three months of start of study
             drug.

          -  Severe hypersensitivity (Grade 3 or higher) to pembrolizumab, lenvatinib, or any of
             their excipients.

          -  Has received prior treatment with any treatment targeting VEGF-directed angiogenesis,
             any anti-PD-1, anti-PD-L1, anti-PD-L2 agent, or with an agent directed to another
             stimulatory or co-inhibitory T-cell receptor (eg, CTLA-4, OX-40, CD137).

          -  Has a known history of active TB (Bacillus Tuberculosis).

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

          -  Bleeding or thrombotic disorders or participants at risk for severe hemorrhage. The
             degree of tumor invasion/infiltration of major blood vessels (e.g., carotid artery)
             should be considered because of the potential risk of severe hemorrhage associated
             with tumor shrinkage/necrosis following lenvatinib therapy.

          -  Participants having > 1+ proteinuria on urine dipstick testing unless a 24-hour urine
             collection for quantitative assessment indicates that the urine protein is <1 g/24
             hours.

          -  Uncontrolled hypertension (Systolic BP>140 mmHg or diastolic BP >90 mmHg) in spite of
             an optimized regimen of antihypertensive medication.

          -  Gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition
             that might affect the absorption of lenvatinib.

          -  Prolongation of corrected QT (QTc) interval to >480 milliseconds (ms).

          -  Serious nonhealing wound, ulcer, or bone fracture.

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

          -  Will need immediate local surgery or radiation for brain metastases.

          -  Unable to undergo MRI.

          -  Electrolyte abnormalities that have not been corrected.

          -  Significant cardiovascular impairment: history of congestive heart failure greater
             than New York Heart Association (NYHA) Class II, unstable angina, myocardial
             infarction or stroke within 6 months of the first dose of study drug, or cardiac
             arrhythmia requiring medical treatment at Screening.