Lenvatinib (E7080/MK-7902) in Combination With Pembrolizumab (MK-3475) vs. Standard Chemotherapy and Lenvatinib Monotherapy in Participants With Recurrent/Metastatic Head and Neck Squamous Cell Carcinoma That Progressed After Platinum Therapy and Immunotherapy (MK-7902-009/E7080-G000-228/LEAP-009)

Inclusion Criteria: * Pathologically confirmed recurrent (not amenable to curative treatment with local and/or systemic therapies) or metastatic (disseminated) head and neck squamous cell carcinoma (HNSCC) of the oral cavity, oropharynx, hypopharynx, and/or larynx that is considered incurable by local therapies * Disease progression at any time during or after treatment with a platinum-containing (e.g., carboplatin or cisplatin) regimen * Disease progression on or after treatment with a programmed cell death protein 1/programmed death-ligand 1 monoclonal antibody (anti-PD-1/PD-L1 mAb) * Pre-study imaging that demonstrates evidence of disease progression based on investigator review of at least 2 pre-study images per RECIST 1.1, following initiation of treatment with a PD-1/PD-L1 inhibitor * Measurable disease by computed tomography scan (CT) or magnetic resonance imaging (MRI) based on Response Criteria in Solid Tumors Version 1.1 (RECIST 1.1) as verified by blinded independent central review (BICR). Tumor lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 assessed within 7 days of the first dose of study intervention * Male participants are eligible to participate if they agree to the following during the intervention period and for at least 1 week after the last dose of lenvatinib, 3 months after the last dose of capecitabine…