• Subjects with CD19+ B-cell lymphoma or B-Cell Acute Lymphoblastic Leukemia (B-ALL) with no currently available curative treatment option (such as autologous or allogeneic Hematopoietic stem cell transplantation (HSCT)) who have a limited prognosis (\<2-year projected survival) will be enrolled. Participation on this trial is permitted as a bridge to HSCT.

• Peripheral blood CD3 count \> 200/µL by flow cytometry. Please note that this test might need to be repeated multiple times as standard practice to optimize collection efficiency.

• Subjects will have a diagnosis of Diffuse Large B Cell Lymphoma (DLBCL), Follicular Lymphoma (FL), Mantle Cell Lymphoma (MCL), CLL, Marginal Zone Lymphoma (MZL), Lymphoplasmacytic Lymphoma (LPL) or B-ALL and will have failed at least 2 lines of therapy in the case of lymphoma and one line if the diagnosis is B-ALL or be refractory (no response or progressive disease) to first line therapy. A line of therapy must include conventional (immuno) chemotherapy (e.g. rituximab, cyclophosphamide, doxorubicin, and prednisone (R-CHOP) or Bendamustine plus Rituximab (BR) in the case of lymphoma) administered for at least 2 cycles. Second or greater lines of therapy must be administered for at least two cycles. Single agent anti-CD20 monoclonal antibody (e.g. rituximab, obinutuzumab) is not considered for the purposes of these criteria to count as a line of therapy. The definition of a line of therapy is taken according to recommended regimens for first and second line therapy in the relevant sections of the National Comprehensive Cancer Network (NCCN) guidelines. The most recent version of the guidelines will be used for eligibility determination. In the unlikely event that a subject received a first or second line regimen no longer listed in the most recent guidelines, but previously present in the version of the guidelines active at the time the therapy was administered, then the subject would be deemed to have received a line of therapy.

• Subjects with pathological and clinical evidence of transformed indolent lymphoma (FL, CLL, MZL or LPL) are eligible for participation on this trial if they have received at least one line of therapy for transformed disease for at least two cycles regardless of response.

• Demonstration of CD19 expression by immunohistochemistry or flow cytometry on a pathological specimen of lymphoma or ALL cells at any time in the course of prior treatment.

• Subjects who are unable to receive commercially available CD19-CAR T-cell therapy.

• Patients with lymphoma must have measurable or assessable disease. Patients in complete remission with no evidence of disease are not eligible.

• Patients with B-ALL must have at least measurable detectable disease on two separate occasions at least 2 weeks apart to be eligible.

• Subjects who relapse at \> 100 days after autologous or allogeneic HSCT are eligible for participation on this trial. Allogeneic HSCT recipients must be off all immunosuppression for a minimum of 4 weeks before leukapheresis is performed and be free of active acute and chronic Graft Versus Host Disease (GVHD).

⁃ Subjects will be ≥ 18 and \< 80 years of age.

⁃ Female subjects of childbearing potential must have a negative urine or serum pregnancy test and if sexually active must use an acceptable method of contraception, including abstinence, a barrier method (diaphragm or condom), Depo-Provera, or an oral contraceptive. Active contraception should continue for at least one year after CAR T-cell infusion.

⁃ Male participants must be willing to practice birth control from the time of enrollment on this study and for 6 months after receiving the preparative regimen.

⁃ Cardiac ejection fraction ≥ 0.45 by MUGA (multigated acquisition) or echocardiography.

⁃ No requirement for supplemental oxygen and no dyspnea at rest. DLCO (diffusing capacity of the lungs for carbon monoxide) and FEV (forced expiratory volume)1 ≥ 0.65 of predicted.

⁃ Karnofsky performance score ≥ 70.

⁃ Subjects must have an expected survival \> 12 weeks.

⁃ Subjects must be able to comprehend the risks and methods used in this clinical trial and independently consent to participate.

⁃ Subjects must consent to anonymous reporting of data to the CIBMTR (Center for International Blood and Marrow Transplant Research).