Human AntiCD19 Chimeric Antigen Receptor T Cells for Relapsed or Refractory Lymphoid Malignancies

Inclusion Criteria: * Must have relapsed or refractory non-Hodgkin lymphoma (NHL) (Group A - NHL/CLL), chronic lymphocytic leukemia (Group A - NHL/CLL) or acute lymphoblastic leukemia (Group B - ALL) treated with at least two lines of therapy. Disease must have either progressed after the last regimen or presented failure to achieve complete remission with the last regimen. * The participant's malignancy is CD19 positive, either by immunohistochemistry or flow cytometry analysis on the last biopsy available or peripheral blood for circulating disease. * Eastern Cooperative Oncology Group (ECOG) Performance status ≤ 2 * Total bilirubin ≤ 1.5 times the institutional upper limit of normal unless bilirubin rise is due to Gilbert's syndrome (maximum 2 time normal) or of non-hepatic origin * AST (SGOT) ≤ 3 times institutional upper limit of normal * ALT (SGPT) ≤ 3 times institutional upper limit of normal * Serum Creatinine ≤ 2 times the institutional upper limit of normal and creatinine clearance ≥ 30 mL/min (calculated or measured) * Must have adequate pulmonary function as defined as pulse oximetry ≥ 92% on room air. * Must have adequate cardiac function as defined as left ventricular ejection fraction≥ 40% in the most recent echocardiogram. * Absolute Lymphocyte Count \>100/microliter (uL) * Participants (or legal guardians) must have the ability to understand and the willingness to sign a written informed consent document. * For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use a contraceptive method with a failure rate of \< 1% per year during the treatment period and for at least 90 days after the human anti-CD19 CAR-T cell infusion. 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, 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. * For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm, as defined below: With female partners of childbearing potential, men must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for at least 6 months after the human anti-CD19 CAR-T cell infusion. Men must refrain from donating sperm during this same period. With pregnant female partners, men must remain abstinent or use a condom during the treatment period and for at least 6 months after the human antiCD19 CAR-T cell infusion to avoid potential embryonal or fetal exposure. 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 Exclusion Criteria: * Autologous transplant within 6 weeks of planned CAR-T cell infusion. * Allogeneic stem cell transplant within 3 months of planned CAR-T cell infusion and patients must be off immunosuppressive agents. * Active graft versus host disease. * Active central nervous system or meningeal involvement by lymphoma or leukemia. Subjects with untreated brain metastases/central nervous system (CNS) disease will be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Participants with a history of CNS or meningeal involvement must be in a documented remission by cerebrospinal fluid (CSF) evaluation and contrast-enhanced MRI imaging for at least 90 days prior to registration. * Second active malignancy, other than non-melanoma skin cancer or carcinoma in situ (e.g. cervix, bladder, breast). * A minimum of 28 days must have elapsed between prior treatment with investigational agent(s) and the day of lymphocyte collection. * HIV seropositivity. * Participants with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, pulmonary abnormalities or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant or breastfeeding women are excluded from this study because CAR-T cell therapy may be associated with the potential for teratogenic or abortifacient effects. Women of childbearing potential must have a negative serum pregnancy test. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with CAR-T cells, breastfeeding should be discontinued. These potential risks may also apply to other agents used in this study. * Evidence of myelodysplasia or cytogenetic abnormality indicative of myelodysplasia on screening bone marrow biopsy prior * Serologic status reflecting active hepatitis B or C infection. Patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment. (PCR positive patients will be excluded.) * Participants with history of clinically relevant CNS pathology such as epilepsy, seizure disorders, paresis, aphasia, uncontrolled cerebrovascular disease, severe brain injuries, dementia and Parkinson's disease. * History of autoimmune disease (i.e. rheumatoid arthritis, systemic lupus erythematosus) with requirement of immunosuppressive medication within 6 months.