A Study of Biomarker-Directed, Pembrolizumab (MK-3475) Based Combination Therapy for Advanced Non-Small Cell Lung Cancer (MK-3475-495/KEYNOTE-495)

Inclusion Criteria: * Has a histologically- or cytologically-confirmed diagnosis of Stage IV (American Joint Committee on Cancer \[AJCC\] v 8) NSCLC and has not had prior systemic therapy for advanced disease * Has confirmation that epidermal growth factor receptor- (EGFR-), anaplastic lymphoma kinase- (ALK-), c-ros oncogene 1- (ROS1-), or B isoform of rapidly accelerated fibrosarcoma- (B-Raf-) directed therapy is not indicated as primary therapy (documentation of absence of tumor activating EGFR mutations, B-Raf mutations, ALK gene rearrangements, and ROS1 gene rearrangements) * Has measurable disease per RECIST 1.1 as assessed by the local site investigator/radiology * Male participants must agree to use contraception during the treatment period and for ≥120 days, after the last dose of study treatment and refrain from donating sperm during this period. Male participants with pregnant partners must agree to use a condom * Female participants eligible to participate if not pregnant, not breastfeeding, and not a woman of childbearing potential (WOCBP) or is a WOCBP who agrees to follow contraceptive guidance during the treatment period and for ≥120 days after the last dose of study treatment * Provided archival tumor tissue sample or newly obtained core or excisional biopsy of a tumor lesion not previously irradiated * Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 * Has adequate organ function Exclusion Criteria: * Has significant cardiovascular impairment within 12 months of the first dose of study drug: history of congestive heart failure greater than New York Heart Association (NYHA) Class II, unstable angina, myocardial infarction or cerebrovascular accident (CVA) stroke, or cardiac arrhythmia associated with hemodynamic instability, significant cardiovascular impairment, or a left ventricular ejection fraction (LVEF) below the institutional normal range as determined by multigated acquisition scan (MUGA) or echocardiogram * Prolongation of QTc interval to \>480 milliseconds (ms) * Has symptomatic ascites or pleural effusion * Has had an allogenic tissue/solid organ transplant * WOCBP who has a positive urine pregnancy test within 24 hours before the first dose of study treatment * Has not recovered adequately from any toxicity and/or complications from major surgery prior to starting therapy, or has had major surgery within 3 weeks prior to first dose of study intervention * Has preexisting ≥Grade 3 gastrointestinal or non-gastrointestinal fistula, gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of lenvatinib * Radiographic evidence of major blood vessel invasion/infiltration * Clinically significant hemoptysis or tumor bleeding within 2 weeks prior to the first dose of study drug * Has received prior systemic chemotherapy treatment for metastatic/recurrent NSCLC * Has current NSCLC disease that can be treated with curative intent with surgical resection, localized radiotherapy, or chemoradiation * Is expected to require any other form of systemic or localized antineoplastic therapy while on study (including maintenance therapy with another agent for NSCLC, radiation therapy, and/or surgical resection) * 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 * Has received previous treatment with another agent targeting the Lymphocyte-activation gene 3 (LAG-3) receptor * Has received previous treatment with another agent targeting vascular endothelial growth factor (VEGF) or the VEGF receptor * Has received prior anticancer therapy including investigational agents within 4 weeks prior to randomization * Has received prior radiotherapy within 2 weeks of start of study treatment or received lung radiation therapy of \>30 Gy within 6 months prior to the first dose of study intervention * Has received a live or live-attenuated 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 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 a known additional malignancy that is progressing or has required active treatment within the past 3 years * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis * Has severe hypersensitivity (≥Grade 3) to pembrolizumab, favezelimab, or lenvatinib and/or any of its excipients * 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) * Has a history of (noninfectious) 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 (defined as hepatitis B surface antigen \[HBsAg\] reactive) or known active hepatitis C virus (defined as HCV RNA \[qualitative\] is detected) infection * Has a known history of active tuberculosis (TB; Bacillus tuberculosis) * 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 known psychiatric or substance abuse disorders that would interfere with cooperating with the requirements of the study * 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 (females and males) after the last dose of study treatment.