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 creatinine or creatinine clearance \[CrCl\]) \>= 60 mL/min GFR or CrCl for subjects with creatinine levels \> 1.5 x institutional ULN, performed within 28 days of treatment initiation * Creatinine clearance will be calculated per institutional standard * Serum total bilirubin =\< 1.5 x ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN, performed within 28 days of treatment initiation * Aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) and alanine aminotransferase (ALT)/serum glutamic pyruvic transaminase (SGPT) =\< 2.5 x ULN OR =\< 5 x ULN for subjects with lymphoma in the liver, performed within 28 days of treatment initiation * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants performed within 28 days of treatment initiation * Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants, performed within 28 days of treatment initiation * Female subject of childbearing potential should have a negative urine or serum pregnancy test within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication; female subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year * Females of reproductive potential enrolled in the lenalidomide cohort must adhere to the scheduled pregnancy testing as required in the Revlimid Risk Evaluation and Mitigation Strategy (REMS) program * Male subjects should agree to use two methods of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy * All study participants enrolled in the lenalidomide containing cohort (cohort 2) must be registered into the mandatory Revlimid REMS program, and be willing and able to comply with the requirements of the REMS program Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study drug or using an investigation device within 4 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment * Has had a prior monoclonal antibody within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events (AEs) due to agents administered more than 4 weeks earlier * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from AEs due to a previously administered agent; \* Note: Subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study * Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that is progressing and requires active treatment; exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy * Has known active central nervous system (CNS) lymphoma and/or lymphomatous meningitis; subjects with previously treated CNS lymphoma and/or lymphomatous meningitis may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment * No active autoimmune disease that has required systemic treatment in past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment; subjects with vitiligo or resolved childhood asthma/atopy would be an exception to this rule; subjects that require intermittent use of bronchodilators, local steroid injections or inhaled or topical steroids would not be excluded from the study; subjects with hypothyroidism stable on hormone replacement or Sjogren's syndrome will not be excluded from the study * Has evidence of interstitial lung disease or active, non-infectious pneumonitis that required steroids or current pneumonitis * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has received prior therapy with an anti-programmed cell death 1 (PD-1), anti-programmed cell death ligand 1 (PD-L1), anti-programmed cell death ligand 2 (PD-L2), anti- cluster of differentiation (CD)137, or anti-cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways) * Note: Subjects that received prior therapy with pidilizumab are an exception to this criterion and may qualify for the study * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B virus surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] qualitative is detected) * Has received a live vaccine within 30 days prior to the first dose of trial treatment