Inclusion Criteria: 1. Age ≥18 years 2. Relapsed or refractory B-cell NHL, including 1. DLBCL cohort (no longer enrolling): DLBCL, not otherwise specified (NOS; includes transformed DLBCL from indolent histology [tDLBCL]), high-grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements with DLBCL histology (Swerdlow 2016), primary mediastinal B-cell lymphoma (PMBCL), and follicular lymphoma Grade 3B. Subjects must have been treated with an anthracycline and rituximab (or other CD20-targeted agent) and have relapsed or refractory disease after at least 2 lines of systemic therapy or after auto-HSCT. 2. MCL cohort: MCL (diagnosis must be confirmed with cyclin D1 expression or evidence of t(11;14) by cytogenetics, fluorescent in situ hybridization [FISH], or PCR) with relapsed or refractory disease after at least 2 prior lines of systemic MCL therapy. Subjects must have been treated with an alkylating agent, Bruton's tyrosine kinase inhibitor (BTKi), and rituximab (or other CD20-targeted agent). 3. PET-positive disease by Lugano classification 4. 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. 5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 6. Adequate bone marrow, renal, hepatic, pulmonary, and cardiac function 7. Adequate vascular access for leukapheresis procedure 8. Participants who have received previous CD19-targeted therapy must have CD19-positive lymphoma confirmed on a biopsy since completing the prior CD19-targeted therapy. 9. Participants must agree to use appropriate contraception. Exclusion Criteria: 1. Active central nervous system (CNS)-only involvement by malignancy (note: participants with secondary CNS involvement are allowed on study) 2. History of other primary malignancy not in remission for at least 2 years (The following are exempt from the 2-year limit: nonmelanoma skin cancer, definitively treated stage 1 solid tumor with low risk for recurrence, curatively treated localized prostate cancer, and cervical carcinoma in situ on biopsy or a squamous intraepithelial lesion on Pap smear) 3. Treatment with alemtuzumab within 6 months of leukapheresis or fludarabine or cladribine within 3 months of leukapheresis 4. Active hepatitis B, hepatitis C, or Subjects with a history of or active human immunodeficiency virus (HIV) infectionare excluded. Subjects with active hepatitis B, or active hepatitis C are also excluded. Subjects with a negative PCR assay for viral load for hepatitis B or C are permitted. Subjects positive for hepatitis B surface antigen and/or anti-hepatitis B core antibody with negative viral load are eligible and should be considered for prophylactic antiviral therapy 5. Uncontrolled systemic fungal, bacterial, viral, or other infection 6. Presence of graft-vs-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. Use of the following: - Therapeutic doses of corticosteroids (defined as >20 mg/day prednisone or equivalent) within 7 days of leukapheresis or 72 hours prior to JCAR017 administration. Physiologic replacement, topical, and inhaled steroids are permitted. - Low dose chemotherapy (e.g., vincristine, rituximab, cyclophosphamide ≤300 mg/m2) given after leukapheresis to maintain disease control must be stopped ≥7 days prior to lymphodepleting chemotherapy. - Cytotoxic chemotherapeutic agents that are not considered lymphotoxic (see below) within 1 week of leukapheresis. Oral chemotherapeutic agents, including lenalidomide and ibrutinib, are allowed if at least 3 half-lives have elapsed prior to leukapheresis. - Lymphotoxic chemotherapeutic agents (e.g., cyclophosphamide, ifosfamide, bendamustine) within 2 weeks of leukapheresis. - Experimental agents within 4 weeks of leukapheresis unless no response or disease progression is documented on the experimental therapy and at least 3 half-lives have elapsed prior to leukapheresis - Immunosuppressive therapies within 4 weeks of leukapheresis and JCAR017 administration (e.g., calcineurin inhibitors, methotrexate or other chemotherapeutics, mycophenolyate, rapamycin, thalidomide, immunosuppressive antibodies such as anti-TNF, anti IL6, or anti-IL6R) - Donor lymphocyte infusions (DLI) within 6 weeks of JCAR017 administration - Radiation within 6 weeks of leukapheresis. Subjects must have progressive disease in irradiated lesions or have additional non-irradiated, PET-positive lesions to be eligible. Radiation to a single lesion, if additional non-irradiated PET-positive lesions are present, is allowed up to 2 weeks prior to leukapheresis. - Allo-HSCT within 90 days of leukapheresis 11. Prior CAR T-cell or other genetically-modified T-cell therapy, with the exception of prior JCAR017 treatment in this protocol for subjects receiving retreatment 12. Progressive vascular tumor invasion, thrombosis, or embolism 13. Venous thrombosis or embolism not managed on a stable regimen of anticoagulation