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 or B-Raf mutations AND absence of
             ALK or 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)

          -  History of transient ischemic attack within the previous 6 months

          -  Has symptomatic ascites or pleural effusion

          -  Has had an allogenic tissue/solid organ transplant

          -  WOCBP who has a positive urine pregnancy test within 72 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

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

          -  Radiographic evidence of major blood vessel invasion/infiltration

          -  Active hemoptysis (bright red blood of at least 0.5 teaspoon) or tumor bleeding within
             3 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 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 3 weeks of start of study treatment

          -  Has received a live vaccine within 30 days prior to 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, MK-4280, 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