Researchers are looking for new ways to treat children with different types of melanoma (skin cancer), solid tumors, and lymphomas (blood cancers) that are any of these: * Advanced, which means cancer spread in the body or cannot be removed with surgery * Relapsed, which means cancer has come back after it had responded to previous treatment (responded means it stopped growing, gets smaller, or disappeared) * Refractory, which means cancer did not respond to previous treatment Pembrolizumab is an immunotherapy, which is a treatment that helps the immune system fight cancer. Researchers want to learn if different doses of pembrolizumab can cause at least 1 of the types of cancer to get smaller or go away. With Amendment 8, enrollment of participants with solid tumors and participants 6 months to under 12 years old with melanoma were closed. With Amendment 13, enrollment was closed for participants with relapsed refractory classical Hodgkin lymphoma (rrCHL), microsatellite instabilty-high (MSI-H) solid tumors, tumor-mutational burden-high (TMB-H) solid tumors, and participants 12 years old to \<18 years old with advanced melanoma.
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Objective Response Rate (ORR) by Response Evaluation Criteria in Solid Tumors and Other Lymphoma Version 1.1 (RECIST 1.1) per Site Assessment (Each Disease Indication Evaluated Separately)
Timeframe: Up to 2 years
ORR by RECIST 1.1 per Site Assessment for MSI-H or TMBH Solid Tumors (Each Cohort Evaluated Separately)
Timeframe: Up to 2 years
ORR by International Working Group (IWG) Response Criteria (Cheson, 2007) per Blinded Independent Central Review (BICR) Assessment for rrcHL Cohort
Timeframe: Up to approximately 2 years
Number of Participants with Dose-Limiting Toxicities (DLTs)
Timeframe: Cycle 1 (Up to 21 days)
Number of Participants Experiencing Adverse Events (AEs)
Timeframe: Up to 27 months
Number of Participants Discontinuing Study Drug Due to AEs
Timeframe: Up to 2 years