Study of Favezelimab (MK-4280) as Monotherapy and in Combination With Pembrolizumab (MK-3475) With or Without Chemotherapy or Lenvatinib (MK-7902) AND Favezelimab/Pembrolizumab (MK-4280A) as Monotherapy in Adults With Advanced Solid Tumors (MK-4280-001)

Inclusion Criteria:

* Part A and Part B: Has histologically or cytologically-confirmed metastatic solid tumor.
* Has measurable disease by immune-related Response Evaluation Criteria in Solid Tumors (irRECIST) 1.1 criteria.
* Has a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale.
* Demonstrates adequate organ function.
* If female, is not pregnant or breastfeeding, and if of child-bearing potential, is willing to use an adequate method of contraception for the course of the study and for at least 180 days after the last dose of chemotherapy, 120 days after the last dose of pembrolizumab or favezelimab, or 30 days after the last dose of lenvatinib, whichever occurs last.
* If male with a female partner(s) of child-bearing potential, both must agree to use an adequate method of contraception starting with the first dose of study drug through 95 days after the last dose of study drug.

Exclusion Criteria:

* Has had chemotherapy, radiation or biological cancer therapy within 4 weeks prior to the first dose of study drug, or has not recovered to Common Terminology Criteria for Adverse Events (CTCAE) Grade 0 or 1 from the AEs due to cancer therapeutics administered more than 4 weeks earlier (this includes participants with previous immunomodulatory therapy with residual immune-related \[ir\]AEs).
* Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of study drug.
* Has received previous treatment with another agent targeting the lymphocyte-activation gene 3 (LAG-3) receptor.
* Has received previous treatment with an immunomodulatory therapy (e.g., anti-programmed cell death-1/anti-programmed cell death-ligand 1 \[anti-PD-1/anti-PD-L1\] or cytotoxic T-lymphocyte-associated protein 4 \[CTLA 4\] agent) and was discontinued from that therapy due to a Grade 3 or higher irAE.
* Is expected to require any other form of antineoplastic therapy while on study.
* Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy in excess of replacement doses, or on any other form of immunosuppressive medication.
* Has a history of a previous, additional malignancy, unless potentially curative treatment has been completed, with no evidence of malignancy for 5 years. Time frame exceptions include successful definitive resection of basal cell carcinoma of the skin, superficial bladder cancer or in situ cervical cancer, or other in situ cancers.
* Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis.
* Has had a severe hypersensitivity reaction to treatment with another monoclonal antibody.
* Has an active autoimmune disease or a documented history of autoimmune disease, except vitiligo or resolved childhood asthma/atopy.
* Has an active infection requiring therapy.
* Has history of (non-infectious) pneumonitis that required steroids or has current pneumonitis.
* Has had a prior stem cell or bone marrow transplant.
* Has a known history of or screens positive for Human Immunodeficiency Virus (HIV), active chronic or acute Hepatitis B or Hepatitis C.
* Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study.
* Is a regular user as determined by investigator judgement (including "recreational use") of any illicit drugs or has a recent history (within the last year) of substance abuse (including alcohol), at the time of signing informed consent.
* Has symptomatic ascites or pleural effusion. A participant who is clinically stable following treatment for these conditions (including therapeutic thoraco- or paracentesis) is eligible.
* Has clinically significant heart disease that affects normal activities.
* Has received a live-virus vaccine within 30 days of planned start of study drug. Seasonal flu vaccines that do not contain live virus are permitted.