Immune Cell Therapy (CAR-T) for the Treatment of Patients With HIV and B-Cell Non-Hodgkin Lymphoma

Inclusion Criteria: * Participant with age \>= 18 years at the time of consent. Because no dosing or adverse event data are currently available on the use of axicabtagene ciloleucel in participants \< 18 years of age, children are excluded from this study * Participant is able to understand and willing to sign a written informed consent document before any study procedures * Participant must have R/R aggressive B-cell NHL of the following histologies: * Diffuse large B-cell lymphoma (DLBCL, including transformed from indolent histology) * High-grade B-cell lymphoma * Primary mediastinal B-cell lymphoma * Follicular lymphoma, grade 3B * Participant must have been treated with an anthracycline and rituximab (or other CD20-targeted agent) and have R/R disease after at least 2 lines of therapy * At least 2 weeks or 5 half-lives, whichever is shorter, must have elapsed since any prior systemic cancer therapy at the time the subject provides consent * Evaluable disease as either: * Positron emission tomography (PET)-positive disease according to the "Recommendations for Initial Evaluation, Staging, and Response Assessment of Hodgkin and Non-Hodgkin Lymphoma: The Lugano Classification", or * Bone marrow involvement assessed by bone marrow biopsy * Eastern Cooperative Oncology Group ECOG performance status =\< 1 (Karnofsky \>= 60%) * Serum creatinine =\< 1.5 x age-adjusted upper limit of normal (ULN) OR calculated creatinine clearance (Cockcroft and Gault) \> 30 mL/…