T Cells Expressing a Fully-human AntiCD19 Chimeric Antigen Receptor for Treating B-cell Malignancies

* INCLUSION CRITERIA: * Malignancy criteria: * Patients with the following malignancies are potentially eligible: any B-cell lymphoma, and chronic lymphocytic leukemia (CLL). Patients with indolent malignancies that have transformed to diffuse large B-cell lymphoma are eligible. * Clear cluster of differentiation 19 (CD19) expression must be uniformly detected on 75% or more of malignant cells from either bone marrow or a leukemia or lymphoma mass by flow cytometry or immunohistochemistry. These assays must be performed at the National Institutes of Health. It is preferable but not required that the specimen used for CD19 determination comes from a sample that was obtained after the patient's most recent treatment. If paraffin embedded unstained samples of bone marrow involved with malignancy or a lymphoma mass are available, these can be shipped to the National Institutes of Health (NIH) for CD19 staining; otherwise, new biopsies will need to be performed for determination of CD19 expression. * Diffuse large B-cell lymphoma (DLBCL) patients must have received at least two prior chemotherapy-containing regimens at least one of which must have contained doxorubicin and a monoclonal antibody. Follicular lymphoma patients must have received at least 2 prior regimens including at least 1 regimen with chemotherapy. All other lymphoma and leukemia patients must have had at least 1 prior chemotherapy-containing regimen. All patients with CLL or small lymphocytic lymphoma must have had prior treatment with ibrutinib or another signal transduction inhibitor. * Patients must have measurable malignancy as defined by at least one of the criteria below. * Lymphoma or leukemia masses that are measurable (minimum 1.5 cm in largest diameter) by computed tomography (CT) scan is required for all diagnoses except CLL. All masses must be less than 10 cm in the largest diameter. * For a lymphoma mass to count as measurable malignancy, it must have abnormally increased metabolic activity when assessed by positron emission tomography (PET) scan. * For CLL and lymphoma with only bone marrow involvement no mass is necessary, but if a mass is not present, bone marrow malignancy must be detectable by flow cytometry in lymphoma and CLL. * Other inclusion criteria: * Greater than or equal to 18 years of age and less than or equal to age 73. * Able to understand and sign the Informed Consent Document. * Clinical performance status of Eastern Cooperative Oncology Group (ECOG) 0-1 * Room air oxygen saturation of 92% or greater * Patients of both genders must be willing to practice birth control from the time of enrollment on this study and for four months after receiving the preparative regimen. * Women of child bearing potential must have a negative pregnancy test because of the potentially dangerous effects of the preparative chemotherapy on the fetus. Women of child-bearing potential are defined as all women except women who are post-menopausal or who have had a hysterectomy. Postmenopausal will be defined as women over the age of 55 who have not had a menstrual period in at least 1 year. * Seronegative for human immunodeficiency virus (HIV) antibody. (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who are HIV seropositive can have decreased immune -competence and thus are less responsive to the experimental treatment and more susceptible to its toxicities.) * Patients with a known history of hepatitis B or hepatitis C are not eligible due to the risk of re-activation of hepatitis after prolonged B-cell depletion due to anti-CD19 CAR T cells. * Seronegative for hepatitis B antigen, positive hepatitis B tests can be further evaluated by confirmatory tests, and if confirmatory tests are negative, the patient can be enrolled. Patients with a known history of hepatitis B are not eligible. * Seronegative for hepatitis C antibody unless antigen negative. If hepatitis C antibody test is positive, then patients must be tested for the presence of ribonucleic acid (RNA) by reverse transcription polymerase chain reaction (RT-PCR) and be hepatitis C virus (HCV) RNA negative. Patients with a known history of hepatitis C are not eligible. * Absolute neutrophil count greater than or equal to 1000/mm(3) without the support of filgrastim or other growth factors. * Platelet count greater than or equal to 45,000/mm(3) without transfusion support * Hemoglobin greater than 8.0 g/dl. * Less than 5% malignant cells in the peripheral blood leukocytes * Serum alanine aminotransferase (ALT) and aspartate aminotransferase (AST) less or equal to 3 times the upper limit of the institutional normal unless liver involvement by malignancy is demonstrated. * Serum creatinine less than or equal to 1.4 mg/dL. * Total bilirubin less than or equal to 2.0 mg/dl. * At least 14 days must have elapsed since any prior systemic therapy prior to apheresis and prior to the initiation of chemotherapy (including systemic corticosteroids at any dose). Because this protocol requires collection of autologous blood cells by leukapheresis in order to prepare CAR T cells, systemic anti-malignancy therapy including systemic corticosteroid therapy of any dose are not allowed within 14 days prior to the required leukapheresis. NOTE: Because of the long half-life and potential to affect CAR T cells, 60 days must elapse from the time of administration of anti-Programmed cell death protein 1 (PD-1) or anti-Programmed death-ligand 1 (PD-L1) antibodies or other agents that in the opinion of the PI can stimulate immune activity and infusion of CAR T cells. * Normal cardiac ejection fraction (greater than or equal to 55% by echocardiography) and no evidence of hemodynamically significant pericardial effusion as determined by an echocardiogram within 4 weeks of the start of the treatment protocol. * Patients must not take corticosteroids including prednisone, dexamethasone or any other corticosteroid for 14 days before apheresis and CAR T-cell infusion. Patients must also not take corticosteroids at doses higher than 5 mg/day of prednisone or equivalent at any time after the CAR T cell infusion. * Patients who have been treated on other protocols of genetically-modified T cells at the NIH only are potentially eligible under these conditions: * At least 6 months have elapsed since the last genetically-modified T-cell therapy that the patient received and there is no evidence of replication-competent retroviruses (evidence must be provided from prior NIH gene-therapy protocol Principal Investigator) and persisting genetically-modified T cells are not detectable in the patient's blood (evidence must be provided by prior NIH gene-therapy protocol Principal Investigator). EXCLUSION CRITERIA: * Patients that require urgent therapy due to tumor mass effects or spinal cord compression. * Patients that have active hemolytic anemia. * Patients with second malignancies in addition to their B-cell malignancy are not eligible if the second malignancy has required treatment (including maintenance therapy) within the past 4 years or is not in complete remission. There are two exceptions to this criterion: successfully treated non-metastatic basal cell or squamous cell skin carcinoma. * Women of child-bearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of the preparative chemotherapy on the fetus or infant. * Active uncontrolled systemic infections (defined as infections causing fevers and infections requiring intravenous antibiotics when intravenous antibiotics have been administered for less than 72 hours), active coagulation disorders or other major uncontrolled medical illnesses of the cardiovascular, respiratory, endocrine, renal, gastrointestinal, genitourinary or immune system, history of myocardial infarction, history of ventricular tachycardia or ventricular fibrillation, active cardiac arrhythmias (active atrial fibrillation is not allowed, resolved atrial fibrillation not requiring current treatment is allowed (anticoagulants count as current treatment) ), active obstructive or restrictive pulmonary disease, active autoimmune diseases such as rheumatoid arthritis. * Patients will not be seen for screening appointments or enrolled on the protocol if they have been hospitalized within the 7 days prior to the screening appointment or the date of protocol enrollment. * Any form of primary immunodeficiency (such as Severe Combined Immunodeficiency Disease). * Systemic corticosteroid steroid therapy of any dose is not allowed within 14 days prior to the required leukapheresis, or the initiation of the conditioning chemotherapy regimen. Corticosteroid creams, ointments, and eye drops are allowed. * History of severe immediate hypersensitivity reaction to any of the agents used in this study. * Patients with current central nervous system (CNS) involvement by malignancy (either by imaging or cerebrospinal fluid involvement or biopsy-proven).