Trial Drug: Cetuximab

This study is designed to assess the safety and efficacy of lenvatinib in combination with pembrolizumab versus standard of care (SOC) chemotherapy, and to also assess the safety and efficacy of lenvatinib monotherapy in participants with recurrent/metastatic head and neck squamous cell carcinoma (R/M HNSCC) that have progressed after platinum therapy and a programmed cell death protein 1 (PD-1) or anti-programmed death ligand 1 (PD-L1) inhibitor. The primary hypothesis is that lenvatinib + pembrolizumab is superior to SOC chemotherapy with respect to ORR per modified Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 as assessed by blinded independent central review.