This is an open-label Phase 1b/2 trial of lenvatinib (E7080) plus pembrolizumab in participants with selected solid tumors. Phase 1b will determine and confirm the maximum tolerated dose (MTD) for lenvatinib in combination with 200 milligrams (mg) (intravenous [IV], every 3 weeks [Q3W]) pembrolizumab in participants with selected solid tumors (i.e. non-small cell lung cancer, renal cell carcinoma, endometrial carcinoma, urothelial carcinoma, squamous cell carcinoma of the head and neck, or melanoma). Phase 2 (Expansion) will evaluate the safety and efficacy of the combination in 6 cohorts at the MTD from Phase 1b (lenvatinib 20 mg/day orally + pembrolizumab 200 mg Q3W, IV).