Inclusion Criteria: - Age ≥ 18 years at the time of consent - Relapsed or refractory B-cell NHL of the following histologies: diffuse large B cell lymphoma (DLBCL) not otherwise specified; includes biopsy-confirmed transformed DLBCL from indolent histologies, high-grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements with DLBCL histology, 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 systemic lines of therapy for DLBCL or after auto-HSCT. - Positron-emission tomography-positive disease by Lugano Classification - Eastern Cooperative Oncology Group performance status of 0 to 1 - Adequate bone marrow, renal, hepatic, pulmonary, cardiac organ function - Adequate vascular access for leukapheresis procedure - Subjects who have received previous CD19-targeted therapy must have CD19-positive lymphoma confirmed on a biopsy since completing the prior CD19-targeted therapy - Subjects must agree to use appropriate contraception. Exclusion Criteria: - Subjects with central nervous system (CNS)-only involvement by malignancy (note: subjects with secondary CNS involvement are allowed on study) - History of prior allogeneic hematopoietic stem cell transplant - Treatment with alemtuzumab within 6 months of leukapheresis, or treatment with fludarabine or cladribine within 3 months of leukapheresis - History of another primary malignancy that has not been in remission for at least 2 years.The following are examples of exceptions from the 2-year limit: nonmelanoma skin cancer, definitively-treated stage 1 solid tumor with a low risk of recurrence, curatively treated localized prostate cancer, and cervical carcinoma in situ on biopsy or a squamous intraepithelial lesion on a Papanicolau smear. - Active hepatitis B or hepatitis C infection at the time of screening - History of or active human immunodeficiency virus infection at the time of screening - Uncontrolled systemic fungal, bacterial, viral or other infection despite appropriate anti-infection treatment at the time of leukapheresis or lisocabtagene maraleucel administration - Presence of acute or chronic graft-versus-host disease - History of clinically significant cardiac conditions within the past 6 months - History or presence of clinically relevant CNS pathology such as epilepsy/seizure, paresis, aphasia, stroke, cerebral edema, severe brain injuries, dementia, Parkinson's disease, cerebellar disease, organic brain syndrome, or psychosis - Pregnant or nursing women - Subject does not meet protocol-specified washout periods for certain prior treatments - Prior CAR T-cell or other genetically modified T-cell therapy - Progressive vascular tumor invasion, thrombosis, or embolism - Venous thrombosis or embolism not managed on stable regimen of anticoagulation - Uncontrolled medical, psychological, familial, sociological, or geographical conditions that do not permit compliance with the protocol; or unwillingness or inability to follow the procedures required in the protocol