A Study of Pembrolizumab (MK-3475) With or Without Lenvatinib (E7080/MK-7902) as First Line (1L) Intervention in a Programmed Cell Death-ligand 1 (PD-L1) Selected Population With Recurrent or Metastatic Head and Neck Squamous Cell Carcinoma (R/M HNSCC) (MK-7902-010/LEAP-010)-China Extension

Inclusion Criteria: * Has histologically confirmed diagnosis of recurrent/metastatic head and neck squamous cell carcinoma (R/M HNSCC) that is considered incurable by local therapies Note: Participants with newly-diagnosed HNSCC must be M1/Stage IV * Has a primary tumor location of oropharynx, oral cavity, hypopharynx, or larynx Note: Primary tumor site of nasopharynx (any histology) or unknown primary tumor (including p16+ unknown primary) are not eligible Contraceptive use by men should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies. If the contraception requirements in the local label for any of the study interventions is more stringent than the requirements above, the local label requirements are to be followed * Male participants agree to use approved contraception during the treatment period for at least 7 days after the last dose of lenvatinib/placebo, or refrain from heterosexual intercourse during this period * Female participants are not pregnant or breastfeeding, and are not a woman of childbearing potential (WOCBP), OR are a WOCBP that agrees to use contraception during the treatment period (or 14 days prior to the initiation of study treatment for oral contraception) and for at least 120 days post pembrolizumab, or 30 days post lenvatinib/placebo, whichever occurs last * Has measurable disease per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) as assessed by blinded independent central review (BICR) Note: Lesions situated in a previously irradiated area are considered measurable if progression has been showed in such lesions * Participants with oropharyngeal cancer must have results from testing of human papillomavirus (HPV) status * Has an Eastern Cooperative Oncology Group (ECOG) performance score of 0 to 1 * Has adequately controlled blood pressure with or without antihypertensive medications * Has adequate organ function Exclusion Criteria: * Has any evidence of symptoms or signs of active tumor bleeding within 6 months before randomization * Has radiographic evidence of major blood vessel invasion/infiltration or tumor demonstrates \>90 degree abutment or encasement of a major blood vessel Note: The degree of proximity to major blood vessels should be considered because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis after lenvatinib therapy * Has a history of re-irradiation to any head and neck sites of disease including the cervical, infraclavicular or supraclavicular lymph nodes for head and neck cancer * Has ulceration and/or fungation of disease onto the skin surface * Has a history of any contraindication or has a severe hypersensitivity to any components of pembrolizumab (≥Grade 3) or lenvatinib * Has pre-existing ≥Grade 3 gastrointestinal or non-gastrointestinal fistula * Has a history of a gastrointestinal condition or procedure that, in the opinion of the investigator, may affect oral study drug absorption * Has clinically significant cardiovascular impairment within 12 months of the first dose of study intervention, such as history of congestive heart failure greater than New York Heart Association (NYHA) Class II, unstable angina, myocardial infarction or cerebrovascular accident/transient ischemic attack (TIA)/stroke, cardiac revascularization, or cardiac arrhythmia associated with hemodynamic instability * Has disease that is suitable for local therapy administered with curative intent * Had PD within 6 months of completion of curatively intended systemic treatment for locoregionally advanced HNSCC * Has had major surgery within 3 weeks before to first dose of study interventions * Has difficulty swallowing capsules or ingesting a suspension orally or by a feeding tube * Has received prior therapy with lenvatinib or pembrolizumab * Received last dose of systemic therapy for locoregionally advanced disease less than 6 months before signing consent * Has received prior therapy with an anti-programmed cell death 1 protein (anti-PD-1), anti-programmed cell death ligand 1 (anti-PD-L1), or anti-programmed cell death ligand 2 (anti PD-L2) agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., CTLA-4, OX-40, CD137) * Has received prior systemic anticancer therapy including investigational agents within 4 weeks before randomization * Has received prior radiotherapy within 2 weeks of start of study intervention * Has received a live vaccine within 30 days before the first dose of study intervention. Administration of killed vaccines is allowed * Has received an investigational agent or has used an investigational device within 4 weeks prior to study intervention-administration * 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 intervention * Has a known additional malignancy that is progressing or has required active treatment within the past 3 years Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g., breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis * Has an active autoimmune disease that has required systemic treatment in past 2 years. Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid) is allowed * Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis * Has an active infection requiring systemic therapy. (e.g., tuberculosis, known viral or bacterial infections, etc.) * 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 ribonucleic acid (RNA) \[qualitative\] is detected) infection * 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 after the last dose of study intervention * Has had an allogenic tissue/solid organ transplant * Has a known psychiatric or substance abuse disorder that would interfere with the participant's ability to cooperate with the requirements of the study