Pomalidomide After CAR T-cell Therapy for the Treatment of Relapsed or Refractory CD19+ B-cell Leukemia or Lymphoma

Inclusion Criteria: * Subject must have had a histologically or cytologically confirmed R/R CD19+ B-cell leukemia or lymphoma and have received a commercially available CAR-T product approved to treat R/R CD19+ Bcell leukemias and lymphomas. * Subject must be 28 - 56 days post infusion of CD19CART product at time of enrollment. * \>= 18 years in age at time of enrollment * Subject is able to swallow pills/tablets * Karnofsky or Lansky performance score of \>= 50% * Absolute neutrophil count (ANC) \>= 750/mm\^3 (granulocyte colony stimulating factor allowed) * Platelets \>= 50,000/mm\^3 (transfusion independent for \>= 7 days, defined as not receiving platelet transfusions for at least 7 days prior to enrollment, unless due to marrow involvement from primary malignancy \[thrombopoietin (TPO) mimetics allowed\]) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) per institution * Alanine aminotransferase (ALT \[serum glutamate pyruvate transaminase (SGPT)\]) =\< 3 x institutional ULN per institution * Serum albumin \>= 2.0 g/dL * Creatinine clearance (Cockcroft-Gault equation) \>= 30 mL/min/1.73 m\^2 * Sexually active females capable of becoming pregnant and males must agree to participate in the pomalidomide Risk Evaluation and Mitigation Strategy (REMS) program * Patients must agree not to donate blood during treatment with pomalidomide and for 4 weeks following discontinuation of the drug because the blood might be given to a pregnant female patient whose fetus must no…