Inclusion Criteria:

          -  Has histologically and/or cytologically confirmed diagnosis of previously untreated,
             locally advanced unresectable or metastatic gastroesophageal adenocarcinoma

          -  Is not expected to require tumor resection during the treatment course

          -  Has gastroesophageal adenocarcinoma that is not HER-2/neu positive

          -  Has measurable disease as defined by RECIST 1.1 by scan with IV contrast as determined
             by the local site investigator

          -  Male participants agree to refrain from donating sperm and agree to either remain
             abstinent from heterosexual intercourse as their preferred and usual lifestyle OR
             agree to use contraception, during the intervention period and for ≥7 days after last
             dose of lenvatinib or 90 days after last dose of chemotherapy-whichever comes last

          -  Female participants not pregnant or breastfeeding are eligible to participate if not a
             women of childbearing potential (WOCBP), or if a WOCBP they either use a contraceptive
             method that is highly effective OR remain abstinent from heterosexual intercourse as
             their preferred and usual lifestyle, and do not donate eggs (ova, oocytes) to others
             or freeze/store for their own use, during the intervention period through 120 days
             after last dose of pembrolizumab, 30 days after last dose of lenvatinib, or 180 days
             after last dose of chemotherapy-whichever occurs last

          -  Has a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG)
             Performance Scale within 3 days prior to the first dose of study treatment

          -  Has adequately controlled blood pressure with or without antihypertensive medications

          -  Has adequate organ function

        Exclusion Criteria:

          -  Has had previous therapy for locally advanced unresectable or metastatic
             gastric/gastroesophageal junction (GEJ) esophageal adenocarcinoma

          -  Has had major surgery within 28 days prior to first dose of study interventions

          -  Has had radiotherapy within 14 days of randomization

          -  Has a known additional malignancy that is progressing or has required active treatment
             within the past 5 years

          -  Has known CNS metastases and/or carcinomatous meningitis

          -  Has severe hypersensitivity (≥Grade 3) to treatment with an monoclonal antibody (mAb)
             or known sensitivity or intolerance to any component of lenvatinib, pembrolizumab,
             study chemotherapy agents and/or to any excipients, murine proteins, or platinum
             containing products

          -  Has had an allogeneic tissue/solid organ transplant

          -  Has perforation risks or significant gastrointestinal (GI) bleeding

          -  Has GI obstruction, poor oral intake (CAPOX participants), or difficulty in taking
             oral medication (CAPOX participants)

          -  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 coinhibitory T-cell receptor

          -  Has received prior therapy with anti- vascular endothelial growth factor (VEGF)
             tyrosine kinase inhibitor or anti-VEGF mAb

          -  Has received a live or live-attenuated vaccine within 30 days before the first dose of
             study drug

          -  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 radiographic evidence of encasement or invasion of a major blood vessel, or of
             intratumoral cavitation

          -  Has inadequate cardiac function

          -  Has a history of (noninfectious) pneumonitis/interstitial lung disease that required
             steroids or has current pneumonitis/interstitial lung disease

          -  Has poorly controlled diarrhea

          -  Has accumulation of pleural, ascitic, or pericardial fluid requiring drainage or
             diuretic drugs within 2 weeks prior to enrollment.

          -  Has peripheral neuropathy ≥Grade 2

          -  Has a known history of human immunodeficiency virus (HIV) or HIV 1/2 antibodies

          -  Has a known history of hepatitis B (defined as HBsAg reactive) or known active
             hepatitis C virus (defined as HCV RNA [qualitative] is detected) infection

          -  Has weight loss of >20% within the last 3 months