Autologous, unselected CD3+ lymphocytes collected from apheresis, transfected with a lentiviral vector containing a 2nd generation chimeric antigen receptor (CAR) consisting of a scFv recognizing CD19 and dual co-stimulatory intracellular signaling domains (4-1BB and CD3ζ).

Anti-CD19/4-1BB/CD3ζ CAR T-cell: autologous, unselected CD3+ lymphocytes collected from whole blood or apheresis, transfected with a lentiviral vector containing a 2nd generation chimeric antigen receptor (CAR) consisting of a scFv recognizing CD19 and dual co-stimulatory intracellular signaling domains (4-1BB and CD3ζ). All patients will receive lymphodepleting, conditioning chemotherapy in the form of cyclophosphamide (500 mg/m2/day) and fludarabine (30 mg/m^2/day) on Days -5, -4, and -3 prior to a CAR T-cell intravenous, single dose administration on Day 0.

Phase 1b: Dose Finding/Escalation Dose Level 1: 0.5 x 10^6/kg Dose Level 2: 1.0 x 10^6/kg Dose Level 3: 2.0 x 10^6/kg

Phase 2: Expansion Patients will receive lymphodepleting chemotherapy as indicated prior to receiving the CAR T-cell intravenous, single dose administration on Day 0 at the RP2D as identified during Phase 1b.

Inclusion Criteria:

1. Have given written informed consent prior to any study-specific procedures; children (defined as 17 years of age or less) require guardian consent.
2. Eastern Cooperative Oncology Group (ECOG) Performance Status 0-2; or Karnofsky > 50%.
3. Age of 2 to 70 years at time of screening.
4. A histologically or cytologically documented, CD19+ non-hodgkin's lymphoma or ALL.
5. At least 1 measurable lesion or FDG-avid disease by positron-emission tomography/computed tomography (PET/CT) for lymphoma patients; quantifiable evidence of ALL in either peripheral blood or bone marrow aspirate.
6. Tumor tissue (archival or recent acquisition) must be available for correlative laboratory studies (such as immunohistochemistry, and others).
7. At least 2 prior systemic therapies and patient must not be eligible for potentially curative standard-of-care therapy.
8. Adequate renal function (defined as Cockroft-Gault creatinine clearance > 50 mL/min) and hepatic function (total bilirubin < 1.5x ULN; and AST/ALT < 3x ULN) unless directly related to malignant disease being treated for on study as demonstrated either by PET/CT imaging or by biopsy and histopathologic confirmation.
9. For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods that result in a failure rate of < 1% per year during the treatment period and for at least 90 days after the last dose of study treatment. A woman is considered to be of childbearing potential if she is postmenarcheal, has not reached a postmenopausal state (≥ 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus). Examples of contraceptive methods with a failure rate of < 1% per year include bilateral tubal ligation, male sterilization, established proper use of hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception.
10. Male participants should agree to not donate sperm during study period (i.e. up to 2 years following CAR T-cell administration).
11. Male participants with reproductive potential must agree to use medical approved contraceptives during the study and for 90 days following the last dose of study treatment.
12. Are reliable and willing to make themselves available for the duration of the study, and are willing to follow study procedures.

Exclusion Criteria:

1. Prior treatment with immunotherapy directly targeting T-cells (except anti-thymocyte globulin [ATG]), CD19-directed antibody-based therapies (except blinatumomab), or other gene therapy products.
2. Received any investigational drug/anti-cancer therapy within 30 days.
3. Concurrent participation in another therapeutic clinical trial.
4. Therapeutic doses of corticosteroids (defined as > 20 mg/day prednisone or equivalent) within 7 days prior to blood collection for CAR T-cell product manufacture.
5. Donor lymphocyte infusion (DLI) within 4 weeks prior to leukapheresis.
6. Salvage or debulking chemotherapy within 1 week prior to blood collection for CAR T-cell product manufacture.
7. Prior central nervous system (CNS) involvement.
8. Unresolved acute toxicity of National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) v4.03 Grade >1 (or baseline, whichever is greater) from prior anticancer therapy. Alopecia and other nonacute toxicities are acceptable.
9. An uncontrolled intercurrent illness including but not limited to ongoing or active infection (including fever within 48 hours of screening), symptomatic congestive heart failure (i.e., New York Heart Association [NYHA] Class 3 or 4), unstable angina pectoris, clinically significant and uncontrolled cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
10. Major surgical procedure within 30 days.
11. Known history of human immunodeficiency virus (HIV) or active infection requiring therapy, or positive tests for hepatitis B surface antigen or hepatitis C ribonucleic acid (RNA).
12. Any vaccination against infectious diseases (e.g., influenza, varicella) within 4 weeks (28 days) of initiation of study treatment.
13. A woman who is pregnant or breastfeeding.