Laboratory Treated T Cells in Treating Patients With Relapsed or Refractory Chronic Lymphocytic Leukemia, Non-Hodgkin Lymphoma, or Acute Lymphoblastic Leukemia

Inclusion Criteria: INCLUSIONS FOR SCREENING AND LEUKAPHERESIS * Patients with CD19 expressing acute lymphoblastic leukemia (ALL), chronic lymphocytic leukemia (CLL) or non-Hodgkin lymphoma (NHL) * Ability to understand and provide informed consent * Not human immunodeficiency virus (HIV) infected INCLUSIONS FOR CAR-T CELL THERAPY * Patients with: * CLL who are beyond first remission and who have failed combination chemoimmunotherapy with regimens containing a purine analogue and anti-CD20 antibody or who were not eligible for such therapy; patients with CLL for whom ibrutinib is now standard first line therapy, must have progressed on ibrutinib; patients with fludarabine refractory disease are eligible; patients may be treated following allogeneic hematopoietic cell transplant (HCT); for the concurrent ibrutinib cohort, patients must agree to continue on or be restarted on ibrutinib and must not have had prior intolerance to ibrutinib that would prevent this; patients managed with prior dose reductions for toxicity will continue at the reduced dose for the remainder of this study * Indolent NHL or mantle cell NHL who are beyond first remission and previously treated with chemoimmunotherapy or who were not eligible for such therapy; patients who have relapsed following autologous or allogeneic HCT are eligible * Aggressive NHL such as diffuse large B-cell lymphoma (DLBCL), who have relapsed or have residual disease following treatment with curative intent; patients…