Efficacy and Safety of Lenvatinib (E7080/MK-7902) Plus Pembrolizumab (MK-3475) for Advanced Melanoma in Anti-Programmed Death-1/Programmed Death-Ligand 1 (PD-1/L1)-Exposed Participants (MK-7902-004/E7080-G000-225/LEAP-004)

Inclusion Criteria: * Has histologically or cytologically confirmed melanoma * Has unresectable Stage III or Stage IV melanoma per American Joint Committee on Cancer (AJCC) staging system version 8 that is not amenable to local therapy * Has the presence of ≥1 measurable lesion by computed tomography (CT) or magnetic resonance imaging (MRI) per RECIST 1.1 as confirmed by BICR. * Has progressed on treatment with an anti-PD-1/L1 monoclonal antibody (mAb) administered either as monotherapy, or in combination with other checkpoint inhibitors or other therapies * Has submitted pre-trial imaging * Has an Eastern Cooperative Oncology Group (ECOG) performance status 0 to 1 * Has provided a baseline tumor biopsy * Has resolution of toxic effect(s) of the most recent prior therapy to Grade 1 or less (except alopecia). If participant received major surgery or radiation therapy of \>30 Gray (Gy), they must have recovered from the toxicity and/or complications from the Intervention * Male participants must agree to use approved contraception during the treatment period and for at least 120 days after the last dose of study intervention and refrain from donating sperm during this period * Female participants are not pregnant and not breastfeeding, and are not a woman of childbearing potential (WOCBP) or are a WOCBP who agrees to follow contraceptive guidance during the treatment period and for at least 120 days after the last dose of study intervention * Has adequate organ function Exclusion Criteria: * 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 before the first dose of study treatment * Has a known additional malignancy that is progressing or requires active treatment * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis * Has ocular melanoma * Has known hypersensitivity to active substances or any of their excipients including previous clinically significant hypersensitivity reaction to treatment with another monoclonal antibody * Has an active autoimmune disease that has required systemic treatment in past 2 years (ie, with use of disease modifying agents, corticosteroids or immunosuppressive drugs) * Has an active infection requiring systemic therapy * Has known history of Human Immunodeficiency Virus (HIV) or HIV 1/2 antibodies * Has known history of or is positive for hepatitis B (hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (HCV RNA qualitative\] is detected) * Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or current pneumonitis/interstitial lung disease * Has a history of active tuberculosis (Bacillus tuberculosis) * Has presence of a gastrointestinal condition including malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of lenvatinib * Has had major surgery within 4 weeks prior to first dose of study interventions (adequate wound healing after major surgery must be assessed clinically, independent of time elapsed for eligibility) * Has a pre-existing Grade ≥3 gastrointestinal or non-gastrointestinal fistula * Has radiographic evidence of major blood vessel invasion/infiltration * Has clinically significant hemoptysis or tumor bleeding within 2 weeks prior to the first dose of study drug * Has clinically significant cardiovascular disease within 12 months from first dose of study drug, including New York Heart Association Class III or IV congestive heart failure, unstable angina, myocardial infarction, cerebral vascular accident, or cardiac arrhythmia associated with hemodynamic instability * Has received prior radiotherapy within 2 weeks of Cycle 1 Day 1 with the exception of palliative radiotherapy to bone lesions, which is allowed if completed 2 weeks prior to Cycle 1 Day 1 * Has received a live vaccine within 30 days before the first dose of study treatment * 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 history or has current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the 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 * Has had an allogeneic tissue/solid organ transplant * Has a known psychiatric or substance abuse disorder that would interfere with cooperation with the requirements of the study