Testing the Addition of an Experimental Medication MK-3475 (Pembrolizumab) to Usual Anti-Retroviral Medications in Patients With HIV and Cancer

Inclusion Criteria: * Histologically or cytologically proven metastatic or locally advanced tumors for which no standard therapy exists, or where standard therapy has failed, or in patients otherwise ineligible for standard therapy, or for an indication that anti-PD-1 therapy has been shown to be effective in studies in HIV-uninfected participants; disease-specific criteria will be applied for certain common cancers and cancers strongly associated with HIV; however, enrollment will not be confined to these tumors * Non-small cell lung cancer (NSCLC) * Metastatic or locally advanced disease that progressed after at least one prior therapy * Note: patients that have actionable molecular targets (e.g., epidermal growth factor receptor \[EGFR\], anaplastic lymphoma kinase \[ALK\], c-ros oncogene 1\[ROS1\] mutations) must have received (when indicated) prior appropriate targeted therapy using Food and Drug Administration (FDA)-approved agents * AIDS-related non-Hodgkin lymphoma and other non-Hodgkin lymphoma * Failed standard first-line therapy; and * Failed autologous stem cell transplant if indicated for histology (i.e diffuse large B-cell lymphoma) or autologous stem cell transplant is not feasible * Classical Hodgkin lymphoma * Relapsed or refractory de novo classical Hodgkin lymphoma having failed standard first-line therapy; and * May have failed to achieve a response or progressed after treatment with brentuximab vedotin or may be brentuximab vedotin naive b…