Inclusion Criteria:  Has histologically or cytologically confirmed melanoma. Has unresectable Stage III or Stage IV melanoma, as per American Joint Committee on Cancer guidelines, not amenable to local therapy.  Has been untreated for advanced or metastatic disease except as follows: a. proto-oncogene B-Raf (BRAF) V600 mutation-positive melanoma may have received standard of care targeted therapy as first-line therapy for advanced or metastatic disease. Participants that do not have a BRAF V600 mutation but did receive BRAF or BRAF/MEKi therapy are eligible to participate in this study after discussion with the medical monitor.  b. Prior adjuvant or neoadjuvant therapy, with targeted therapy or immunotherapy (such as anti-cytotoxic T-lymphocyte-associated protein 4 [CTLA-4], anti-programmed cell death 1 [anti-PD-1] therapy or interferon) will only be permitted if relapse did not occur during active treatment or within 6 months of treatment discontinuation.  Have documentation of BRAF V600-activating mutation status or consent to BRAF V600 mutation testing during the Screening period (participants with BRAF mutation-positive melanoma as well as BRAF wild-type or unknown are eligible). Has an Eastern Cooperative Oncology Group (ECOG) performance status 0 to 1. Has the presence of ≥1 measurable lesion by computed tomography (CT) or magnetic resonance imaging (MRI) per RECIST 1.1. Provides a tumor biopsy. Participants must submit tumor sample during Screening for confirmation of adequacy of tumor tissue at a central pathology laboratory. Participants who do not submit a tumor tissue sample will not be randomized. The tumor biopsy may not be obtained from a lone target lesion. Confirmation of presence of tumor tissue is not required prior to randomization. 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 contraception 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.  Female participants must not be pregnant, not breastfeeding, and ≥1 of the following conditions applies:  Not a woman of childbearing potential (WOCBP) OR A WOCBP who agrees to use study-approved contraception during the treatment period and for at least 120 days after the last dose of study treatment. The participant (or legally acceptable representative) has provided documented informed consent for the study. Has adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP ≤150/90 mmHg at screening and no change in antihypertensive medications within 1 week before Cycle 1 Day 1. 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.  Exceptions include early stage cancers (carcinoma in situ or Stage 1, non-ulcerated primary melanoma <1 mm in depth with no nodal involvement) treated with curative intent, basal cell carcinoma of the skin, squamous cell carcinoma of the skin, in situ cervical cancer, or in situ breast cancer that has undergone potentially curative therapy.  Has known active central nervous system 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 (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 systemic treatment. Has an active infection requiring systemic therapy. Has known history of human immunodeficiency virus (HIV) infection. Has known history of or is positive for hepatitis B virus or hepatitis C virus infection. Has a history of (non-infectious) pneumonitis that required steroids or current pneumonitis. Has a history of active tuberculosis (Bacillus tuberculosis). Has presence of gastrointestinal condition including malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of lenvatinib. Has had a major surgery within 4 weeks prior to Cycle 1 Day 1. Adequate wound healing after major surgery must be assessed clinically and have resolved completely prior to Cycle 1 Day 1. 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 treatment. Has clinically significant cardiovascular disease within 12 months of the first dose of study treatment 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 urine protein ≥1 g/24-hour. Note: Participants with ≥2+ (≥100 mg/dL) proteinuria on urine dipstick testing (or urinalysis) will undergo 24-hour urine collection for quantitative assessment of proteinuria. Prolongation of QTcF interval to >480 ms. Note: If the QTcF is prolonged to >480 ms in the presence of a pacemaker, contact the Sponsor to determine eligibility. Has left ventricular ejection fraction (LVEF) below the institutional (or local laboratory) normal range, as determined by multigated acquisition scan (MUGA) or echocardiogram. Has received prior therapy in the adjuvant setting. Note: Targeted therapy, anti-CTLA-4, or anti-PD-1 may be allowed. Has received prior systemic treatment for unresectable or metastatic melanoma other than targeted therapy as noted in Inclusion Criteria above. Has received prior therapy with a monoclonal antibody, chemotherapy, or an investigational agent or device within 4 weeks or 5 half-lives (whichever is longer) before administration of study treatment or not recovered (≤Grade 1 or at Baseline) from adverse events due to previously administered agents.  Exception to this rule would be use of denosumab, which is not excluded. Note: Participants with alopecia and ≤Grade 2 neuropathy are an exception and may enroll.  Has received prior radiotherapy within 2 weeks of first dose of study treatment (Cycle 1 Day 1). Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. Has received 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 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. 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.