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