Testing the Addition of Lenalidomide and Nivolumab to the Usual Treatment for Primary CNS Lymphoma

Inclusion Criteria: * Histologically proven primary CNS diffuse large b-cell lymphoma confirmed by one of the following: * Brain biopsy or resection * Cerebrospinal fluid * Vitreous fluid * No prior organ transplantation to exclude post-transplant lymphoproliferative disorders * No prior chemotherapy or radiation therapy for lymphoma * No prior allogeneic stem cell transplantation * Use of systemic corticosteroids (dexamethasone up to 24 mg/day or equivalent) for disease control or improvement of performance status to be tapered as fast as clinically safe after initiation of therapy is permissible * Not pregnant and not nursing, because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown and an agent that has known genotoxic, mutagenic and teratogenic effects. Therefore, female of childbearing potential (FCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) =\< 7 days prior to registration * Age \>= 18 years * Karnofsky performance scale (KPS) \>= 40 (\>= 50 for patients older than 60 unless related to lymphoma on investigator's opinion) * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Calculated creatinine clearance \>= 50 mL/min by Cockcroft-Gault formula * Total Bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) / alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN) * No evidence of non-Hodgkin's lymphoma (NHL) outside CNS * No prior history of NHL * No history of autoimmune disorder. Patients with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids, should be excluded. These include but are not limited to patients with a history of immune related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia gravis; systemic autoimmune disease such as Systemic lupus erythematosus (SLE), connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, hepatitis; and patients with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded because of the risk of recurrence or exacerbation of disease. Patients with vitiligo, endocrine deficiencies including thyroiditis managed with replacement hormones including physiologic corticosteroids are eligible. Patients with rheumatoid arthritis and other arthropathies, Sjogren's syndrome and psoriasis controlled with topical medication and patients with positive serology, such as antinuclear antibodies (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible * Patients are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger (precipitating event) * Patients should be excluded if they have a condition requiring systemic treatment with either corticosteroids (except short course of systemic corticosteroids for disease control or improvement of performance status or other immunosuppressive medications within 14 days prior to registration. Inhaled or topical steroids and adrenal replacement doses \< 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. Patients are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption). Physiologic replacement doses of systemic corticosteroids are permitted, even if \< 10 mg/day prednisone equivalents. A brief course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by contact allergen) is permitted * Patients who have had evidence of active or acute diverticulitis, intra-abdominal abscess, gastrointestinal (GI) obstruction and abdominal carcinomatosis which are known risk factors for bowel perforation should be evaluated for the potential need for additional treatment before coming on study * No prior or concurrent malignancies with exception of surgically cured carcinoma in situ (CIS) of the uterus, carcinoma of the skin without evidence of disease for \>= 5 years * No concurrent malignancy requiring active therapy * No untreated hepatitis C virus (HCV) infection with detectable HCV viral load * No untreated chronic hepatitis B virus (HBV) infection with detectable HBV viral load * No untreated human immunodeficiency virus (HIV) infection or with detectable viral load or with CD4+T-cell count of less than 500/mm\^3 * No history of HIV infection and evidence of Epstein Barr virus (EBV)-related primary central nervous system lymphoma (PCNSL) * Inability to tolerate anticoagulation with acetylsalicylic acid, warfarin, or direct oral anticoagulants * No other investigational agent * No history of severe hypersensitivity reaction to any monoclonal antibody * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to or other agents used in study * Sulfonamide drugs, trimethoprim, salicylates, nonsteroidal anti-inflammatory drugs, penicillin, vitamin C, ciprofloxacin, and proton pump inhibitors should be held at least 48 hours prior to methotrexate administration