Rituximab and Pembrolizumab With or Without Lenalidomide in Treating Patients With Relapsed Follicular Lymphoma and Diffuse Large B-Cell Lymphoma

Inclusion Criteria: * For cohort 1: Male or female subjects with histologic proof of follicular lymphoma grade 1, 2, or 3a relapsing after at least one prior systemic therapy that included rituximab (or other monoclonal CD20 antibody); patients should have documented rituximab-sensitive disease defined as a documented complete or partial response lasting at least 6 months after the last rituximab-containing therapy * For cohort 2: Male or female subjects with histologic proof of follicular lymphoma grade 1, 2, or 3a relapsing after at least two prior systemic therapies, which must include CAR T cell therapy or histologic proof of DLBCL relapsing after at least two prior systemic therapies, which must include CAR T cell therapy * Either the subject or his/her legally authorized representative be willing and able to provide written informed consent for the trial * Have measurable disease (\>= 1.5 cm in the longest diameter for nodal or extranodal disease) * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L, performed within 28 days of treatment initiation * Platelets \>= 50 x 10\^9/L, performed within 28 days of treatment initiation * Hemoglobin \>= 8.0 g/dL, performed within 28 days of treatment initiation * Serum creatinine =\< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of …