Long-term Safety and Efficacy Extension Study for Participants With Advanced Tumors Who Are Currently on Treatment or in Follow-up in a Pembrolizumab (MK-3475) Study (MK-3475-587/KEYNOTE-587)

The purpose of this study is to evaluate the long-term safety and efficacy of pembrolizumab (MK-3475) in participants from previous Merck pembrolizumab-based parent studies who transition into this extension study. This study will consist of three phases: 1) First Course Phase, 2) Survival Follow-up Phase or 3) Second Course Phase. Each participant will transition to this extension study in one of the following three phases, depending on the study phase they were in at the completion of the parent study. Participants who were in the First Course Phase of study treatment with pembrolizumab or lenvatinib in their parent study will enter the First Course Phase of this study and complete up to 35 doses or more every 3 weeks (Q3W) or 17 doses or more every 6 weeks (Q6W) of study treatment with pembrolizumab or a pembrolizumab-based combination or lenvatinib according to arm assignment. Participants who were in the Follow-up Phase in the parent study (post-treatment or Survival Follow-up Phase) will enter the Survival Follow-up Phase of this study. Participants who were in the Second Course Phase in their parent study will enter Second Course Phase of this study and complete up to 17 doses Q3W or 8 doses Q6W of study treatment with pembrolizumab or a pembrolizumab-based combination according to arm assignment. Any participant originating from a parent trial where crossover to pembrolizumab was permitted upon disease progression may be eligible for 35 doses as Q3W or 17 doses Q6W of pembrolizumab (approximately 2 years), if they progress while on the control arm and pembrolizumab is approved for the indication in the country where the potential eligible crossover participant is being evaluated.

Inclusion Criteria: * Treated on the parent pembrolizumab studies established by the Sponsor as MK-3475-587 ready. * Currently receiving pembrolizumab, pembrolizumab based combinations or lenvatinib from parent studies or in a follow-up phase. Additional eligibility criteria for participants who enter Second Course Phase once they are enrolled on MK-3475-587: * Has not received any anticancer systemic treatment since the last dose of pembrolizumab or a pembrolizumab-based combination in First Course Phase. * Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Demonstrates adequate organ function. * Have resolution of any toxic effect(s) of First Course Phase trial treatment with pembrolizumab or a pembrolizumab-based combination to Grade 1 or less (except alopecia) before trial treatment in Second Course Phase is started. If participant received major surgery or radiation therapy of \>30 Gray (Gy), they must have recovered from the toxicity and/or complications of the intervention. * A female participant is eligible to enroll if she is not pregnant, not breastfeeding, and ≥1 of the following conditions applies: A woman of childbearing potential (WOCBP) who agrees to use contraception during the study treatment period and for ≥120 days (corresponding to time needed to eliminate any study combination treatment(s) plus 30 days (a menstruation cycle) for study treatments with risk of genotoxicity. Additional eligibility criteria for participants who enter dosing with Lenvatinib: * Adequately controlled blood pressure (BP) to \6 \[class B and C\]). * Has uncontrolled thyroid dysfunction. * Has uncontrolled diabetes mellitus. * Has had an allogeneic tissue/solid organ transplant. * Has a known history of active tuberculosis (TB; Bacillus tuberculosis). Additional exclusion criteria for participants who enter dosing with Lenvatinib: * Has had major surgery within 3 weeks prior to first dose of study intervention(s). * Has preexisting ≥Grade 3 gastrointestinal or non-gastrointestinal fistula. * Has urine protein ≥1 g/24 hours. * Has LVEF below the institutional (or local laboratory) normal range, as determined by multigated acquisition scan (MUGA) or echocardiogram (ECHO). * Has radiographic evidence of encasement or invasion of a major blood vessel, or of intratumoral cavitation. * Prolongation of QT intervals corrected for heart rate using Fridericia's (cube root) correction (QTcF) interval to \>480 ms. * Has clinically significant cardiovascular disease within 12 months from first dose of study intervention, including New York Heart Association Class III or IV congestive heart failure, unstable angina, myocardial infarction, cerebral vascular accident, or cardiac arrhythmia associated with hemodynamic instability. * Gastrointestinal malabsorption or any other condition that might affect the absorption of lenvatinib. * Active hemoptysis (bright red blood of at least 0.5 teaspoon) within 3 weeks prior to the first dose of study drug. * Has a history of any contraindication or has a severe hypersensitivity to any components of lenvatinib.