A Clinical Study of MK-1045 in People With Non-Hodgkin Lymphoma (MK-1045-008)

Inclusion Criteria: The main inclusion criteria include but are not limited to the following: * Has disease that has relapsed (disease progression after remission) or is refractory (failure to achieve complete or partial response) to at least 2 prior systemic lines of therapy. * Has a histologically confirmed diagnosis of follicular lymphoma (FL) or diffuse large B-cell lymphoma (DLBCL). * DLBCL participants only: has progressed after or is ineligible for transplant and chimeric antigen receptor T (cell) (CAR-T) therapy. * Has provided tumor tissue sample (archival or newly obtained, if performed per standard of care). * Has documented retained expression of cluster of differentiation 19 (CD19) in tumor tissue obtained by biopsy after disease progression on CD19-targeting therapy, if experienced disease progression after prior CD19-targeting therapy. * Has well-controlled human immunodeficiency virus (HIV) on antiretroviral therapy if has a history of HIV infection. * Has undetectable hepatitis B virus (HBV) viral load and received and will continue to receive HBV antiviral therapy if hepatitis B surface antigen (HBsAg)-positive. * Has undetectable hepatitis C virus (HCV) viral load and received HCV antiviral therapy if has a history of HCV infection. * Has radiographically measurable disease per Lugano Response Criteria. Exclusion Criteria: The main exclusion criteria include but are not limited to the following: * Has received a solid organ transplant. * Had or has clinically relevant central nervous system (CNS) diseases. * Has a history of serious cardiovascular or cerebrovascular diseases. * Had prior allogenic stem cell transplantation with acute graft-versus-host-disease (GVHD); has ongoing evidence of chronic GVHD manifesting as skin involvement, diarrhea, or increased serum bilirubin; or requires systemic immunosuppression for GVHD. * Is HIV-infected with a history of Kaposi's sarcoma and/or Multicentric Castleman's Disease. * Has received a live or live-attenuated vaccine within 30 days of randomization. * Has received prior CAR-T therapy within 3 months before the first dose of the study intervention. * Has a known additional malignancy that is progressing or required active treatment within the past 2 years. * Has known active CNS lymphoma or involvement. * Has active autoimmune disease that required systemic treatment in the past 2 years. * Has active infection requiring systemic therapy. * Has a history of severe bleeding disorders. * Has not recovered from major surgery or has ongoing surgical complications. * Has diagnosis of primary mediastinal B-cell lymphoma.