Dose-escalation Study of Safety of PBCAR20A in Subjects With r/r NHL or r/r CLL/SLL

Key Inclusion Criteria Criteria for NHL: * r/r CD20+ B-cell NHL that is histologically confirmed by archived tumor biopsy tissue from the last relapse and corresponding pathology report. * Measurable or detectable disease according to the Lugano classification. * Primary refractory disease or r/r disease after a response to 2 prior regimens. Criteria for CLL/SLL: * Diagnosis of CD20+ CLL with indication for treatment based on the iwCLL guidelines and clinically measurable disease or SLL with measurable disease that is biopsy-proven SLL. * Previously failed/tolerant to at least 2 prior lines of systemic targeted therapy of known benefit. Criteria for both NHL and CLL/SLL: * Study participant has an Eastern Cooperative Oncology Group (ECOG) Performance Status score of 0 or 1. * Study participant has adequate bone marrow, renal, hepatic, pulmonary, and cardiac function. Key Exclusion Criteria: Criteria for NHL: * Requirement for urgent therapy due to mass effects such as bowel obstruction, spinal cord, or blood vessel compression. * Active central nervous system (CNS) disease. A negative computed tomography (CT)/magnetic resonance imaging (MRI) is required at Screening if the study participant has a history of CNS lymphoma. Criteria for NHL and CLL/SLL: * Active CNS disease. A negative lumbar puncture is required at Screening if the study participant has a history of CNS disease. * Previous malignancy, besides the malignancies of inclusion (B-cell NHL or CLL/SLL), that in the investigator's opinion, has a high risk of relapse in the next 2 years. * Active uncontrolled fungal, bacterial, viral, protozoal, or other infection. * Any form of primary immunodeficiency. * History of human immunodeficiency virus (HIV) infection. * Active hepatitis B or C. * Uncontrolled cardiovascular disease. * Hypertension crisis or hypertensive encephalopathy within 3 months prior to Screening. * Presence of a CNS disorder that renders ineligible for treatment. * History of a genetic syndrome such as Fanconi anemia, Kostmann syndrome, Shwachman Diamond syndrome, or any other known bone marrow failure syndrome. * Received ASCT within 45 days of Screening if the study participant has met the rest of the count requirements. * Must not have received systemic corticosteroid therapy for at least 7 days prior to initiating lymphodepletion chemotherapy. * Received a live vaccine within 4 weeks before Screening. * Radiotherapy within 4 weeks determined on a case-by-case basis. * Presence of a pleural/peritoneal/pericardial catheter. * Current use of any anticoagulant or antiplatelet therapy.