Study Evaluating the Safety and Efficacy of JWCAR029 in Adult Subjects With Relapsed and Refractory B-cell Non-Hodgkin Lymphoma

Inclusion Criteria: * Subjects must meet all of the following criteria to be enrolled in this study: 1. Age ≥ 18 years at the time of consent 2. Signed written informed consent obtained prior to any study procedures 3. Relapsed or refractory B-cell NHL. 4. PET-positive disease BY Lugano classification 5. Archived tumor biopsy tissue available from the last relapse and corresponding pathology report available or, if at least one tumor-involved site is deemed accessible at time of screening, willing to undergo pre-treatment biopsy (excisional when possible) for disease confirmation. If a subject has never had a complete response, a sample from the most recent biopsy is acceptable. 6. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. 7. Adequate bone marrow, renal, hepatic, pulmonary and cardiac function 8. Adequate vascular access for leukapheresis procedure 9. Subjects who have received previous CD19-targeted therapy must have CD19-positive lymphoma confirmed on a biopsy since completing the prior CD19-targeted therapy 10. Subjects must agree to use appropriate contraception. Exclusion Criteria: * Subjects who meet any of the following criteria will be excluded from participation in this study: 1. Subjects with central nervous system (CNS)-only involvement by malignancy (note: subjects with secondary CNS involvement are allowed on study) 2. History of another primary malignancy that has not been in remission for at least 2 years. 3. Treatment with alemtuzumab within 6 months of leukapheresis, or treatment with fludarabine or cladribine within 3 months of leukapheresis 4. Active hepatitis B, hepatitis C, or human immunodeficiency virus (HIV) infection at the time of screening 5. Subjects with uncontrolled systemic fungal, bacterial, viral or other infection despite appropriate antibiotics or other treatment at the time of leukapheresis or JWCAR029 administration 6. Presence of acute or chronic graft-versus-host disease (GVHD) 7. History of cardiovascular disease 8. History or presence of clinically relevant CNS pathology such as epilepsy, seizure, paresis, aphasia, stroke, severe brain injuries, dementia, Parkinson's disease, cerebellar disease, organic brain syndrome, or psychosis 9. Pregnant or nursing women. 10. Prior CAR T-cell or other genetically-modified T-cell therapy, with the exception of prior JWCAR029 treatment in this protocol for subjects receiving retreatment