Lenalidomide and Ipilimumab After Stem Cell Transplant in Treating Patients With Hematologic or Lymphoid Malignancies

Inclusion Criteria: * Hematologic or lymphoid malignancy * Autologous patients can be included anytime within 6 months post-transplant, if they had no signs of progression and meet one of the following criteria: i. leukemia; ii. lymphoma (all types of B and T cell lymphoma); iii. multiple myeloma * Allogeneic patients if: i. patients had engrafted donor cells (i.e., \> 20% donor T-cell from peripheral blood \[PB\]/polymerase chain reaction \[PCR\]); and, ii. patients NOT in complete remission (CR) after their allogeneic transplant, and off tacrolimus and/or mycophenolate mofetil for at least 3 to 4 weeks with no signs of GVHD; or, iii. patients had evidence of relapse after their transplant who are off tacrolimus and/or mycophenolate mofetil or other immunosuppressants for GVHD for 3 to 4 weeks with no signs of GVHD (prednisone doses =\< 10 mg are permitted as stated previously) * No active infection * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L * Platelets \> 75 x 10\^9/L * Able to adhere to the study visit schedule and other protocol requirements * Performance status: Eastern Cooperative Oncology Group (ECOG) 2 or less or Karnofsky of at least 60 * Cardiac ejection fraction (EF) \>= 45% by 2-dimensional echocardiogram (2D-ECHO) within 3 months of study entry (or within 1 month if received chemotherapy within the past 3 months) * Forced expiratory volume in one second (FEV1), forced vital capacity (FVC) and diffusing capacity of the lung for carbon monoxide (DLCO) \>= 40% within 3 months of study entry (or within 1 month if received chemotherapy within the past 3 months) * Serum creatinine =\< 1.6 mg/dL and creatinine clearance \>= 30 ml/min; creatinine clearance will be calculated using the Cockcroft-Gault equation * Serum glutamate pyruvate transaminase (SGPT), serum glutamic oxaloacetic transaminase (SGOT) less than 2 x the upper limit of normal range (unless related to Gilbert's disease or medications) * Direct bilirubin \< 1.6 (unless related to Gilbert's disease or medications) * Patient or legally authorized representative able to sign informed consent * Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 50 mIU/mL within 10-14 days prior to study entry Exclusion Criteria: * Immunotherapy or chemotherapy with approved or investigational anticancer therapeutics within 4 weeks of first dose * Patients on alemtuzumab within 6 weeks prior to consenting * Active congestive heart failure (New York Heart Association \[NYHA\] class III to IV), symptomatic ischemia or conduction abnormalities uncontrolled by conventional interventions; myocardial infarction within 6 months of study entry * Deep vein thrombosis or pulmonary embolism within 3 months of study entry * Pregnant or breast-feeding females; (lactating females must agree not to breast-feed while taking lenalidomide) * Acute active infection requiring intravenous antibiotics, antiviral (except antiviral directed at hepatitis B), or antifungal agents within 14 days of first dose * Known human immunodeficiency virus (HIV) seropositive, hepatitis C infection, and/or hepatitis B (except for patients with hepatitis B surface antigen \[Sag\] or core antibody receiving and responding to antiviral therapy directed at hepatitis B: these patients are allowed) * Patients with other known malignancies within the past three years except: i. adequately treated basal or squamous cell skin cancer; ii. carcinoma in situ of the cervix; iii. prostate cancer with Gleason score \< 6 with stable prostate-specific antigen (PSA) over the past three months; iv. breast cancer in situ with full surgical resection * Significant neuropathy (grades 3 to 4 or grade 2 pain) * Known hypersensitivity to thalidomide, lenalidomide or ipilimumab * Active life-threatening autoimmune disease * Active GVHD or recent GVHD and still on \> 10 mg prednisone (or equivalent) * Prior auto-immune disease