Anakinra for the Reduction of CAR-T Toxicity in Patients With Relapsed or Refractory Large B-cell Lymphoma

Inclusion Criteria: * Relapsed or refractory diffuse large B-cell lymphoma (DLBCL), primary mediastinal B-cell lymphoma (PMBCL), transformed follicular lymphoma (tFL), or high-grade B-cell lymphoma (HGBCL), at least 2 prior lines of systemic therapy * Planned to receive standard of care therapy with axicabtagene ciloleucel * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Measurable disease of \>= 1.5 cm * At least two weeks or 5 half-lives, whichever is shorter, must have elapsed since any prior systemic therapy at the time the subject is planned for axicabtagene ciloleucel (axi-cel) therapy, except for systemic immune checkpoint inhibitory / immune stimulatory therapy. At least 3 half-lives must have elapsed from any prior systemic immune checkpoint inhibitory / immune stimulatory therapy at the time the subject is planned for leukapheresis (e.g. ipilimumab, nivolumab, pembrolizumab, atezolizumab, OX40 agonists, 4-1BB agonists, etc) * Toxicities due to prior therapy must be stable and recovered to =\< grade 1 (except for clinically non-significant toxicities such as alopecia) * Absolute neutrophil count of \>= 1.0 x 10\^9/L * Platelet count of \>= 60 x 10\^9/L * Creatinine clearance (as estimated by Cockcroft Gault) \>= 45 mL/minute (min) * Serum alanine transaminase (ALT) / aspartate transaminase (AST) =\< 2.5 upper limit of normal (ULN) * Total bilirubin =\< 1.5 mg/dL, except in subjects with Gilbert's syndrome * Cardiac ejection fraction \>= 50% with no evidence of pericardial effusion * Baseline oxygen saturation \> 92% on room air * No evidence, suspicion, and/or history of lymphoma involving the central nervous system (CNS) * Females of childbearing potential must have a negative serum or urine pregnancy test (females who have undergone surgical sterilization or who have been postmenopausal for at least 2 years are not considered to be of childbearing potential) Exclusion Criteria: * History of malignancy other than nonmelanoma skin cancer or carcinoma in situ (e.g. cervix, bladder, breast) unless disease free for at least 3 years * History of Richter's transformation of chronic lymphocytic leukemia (CLL) * Autologous stem cell transplantation within 6 weeks of planned axi-cel infusion * History of allogeneic stem cell transplantation * Prior CD19 targeted therapy * Prior chimeric antigen receptor therapy or other genetically modified T cell therapy * Presence of fungal, bacterial, viral, or other infection that is uncontrolled or requiring IV antimicrobials for management. Simple urinary tract infection (UTI) and uncomplicated bacterial pharyngitis are permitted if responding to active treatment and after consultation with the principal investigator * Known history of infection with human immunodeficiency virus (HIV) or hepatitis B (hepatitis B virus surface antigen \[HBsAg\] positive) or hepatitis C virus (anti-HCV positive). A history of hepatitis B or hepatitis C is permitted if the viral load is undetectable per quantitative polymerase chain reaction (PCR) and/or nucleic acid testing * Known history of tuberculosis. A negative Quantiferon or purified protein derivative (PPD) up to 2 months before start of anakinra is enough if no specific risk factors * Presence of any indwelling line or drain (e.g., percutaneous nephrostomy tube, indwelling foley catheter, biliary drain, or pleural/peritoneal/pericardial catheter). Dedicated central venous access catheters such as a Port-a-Cath or Hickman catheter are permitted * Subjects with detectable cerebrospinal fluid malignant cells, or brain metastases, or with a history of CNS lymphoma, cerebrospinal fluid malignant cells or brain metastases * History or presence of CNS disorder such as seizure disorder, cerebrovascular ischemia/hemorrhage, dementia, cerebellar disease, or any autoimmune disease with CNS involvement * Subjects with cardiac atrial or cardiac ventricular lymphoma involvement * History of myocardial infarction, cardiac angioplasty or stenting, unstable angina, or other clinically significant cardiac disease within 12 months of enrollment * Requirement for urgent therapy due to tumor mass effects such as bowel obstruction or blood vessel compression * Primary immunodeficiency * History of autoimmune disease (e.g. Crohn's, rheumatoid arthritis, systemic lupus) resulting in end organ injury or requiring systemic immunosuppression/systemic disease modifying agents within the last 2 years * History of symptomatic deep vein thrombosis or pulmonary embolism within 6 months of enrollment * Any medical condition likely to interfere with assessment of safety or efficacy of study treatment * History of severe immediate hypersensitivity reaction to any of the agents used in this study, including E coli-derived proteins * Live vaccine =\< 6 weeks prior to planned start of conditioning regimen * Women of child-bearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of the preparative chemotherapy on the fetus or infant * Subjects of both genders who are not willing to practice birth control from the time of consent through 6 months after the completion of anakinra injections * In the investigator's judgment, the subject is unlikely to complete all protocol-required study visits or procedures, including follow-up visits, or comply with the study requirements for participation Trial Treatments