NKTR-255 in Combination With CAR-T Cell Therapy for the Treatment of Relapsed or Refractory Large B-cell Lymphoma

Inclusion Criteria: * Male or female \>= 18 years of age at the time of consent * Patients with LBCL (including diffuse large B-cell lymphoma \[DLBCL\] not otherwise specified \[including DLBCL arising from indolent lymphoma\], high-grade B-cell lymphoma, primary mediastinal large B-cell lymphoma, and follicular lymphoma grade 3B) with a Food and Drug Administration (FDA)-approved indication for treatment with liso-cel * Fludeoxyglucose F-18 (FDG)-avid disease on positron emission tomography (PET) imaging or pathology evidence of active disease * Evidence of CD19 expression on any prior or current tumor specimen or a high likelihood of CD19 expression based on disease histology * Karnofsky performance status \>= 60% * Absolute neutrophil count (ANC) \>= 1000 cells/mm\^3 in the absence of bone marrow involvement by lymphoma * Platelets \>= 50,000 cells/mm\^3 in the absence of bone marrow involvement by lymphoma * Hemoglobin \>= 8 g/dL in the absence of bone marrow involvement by lymphoma * Calculated creatinine clearance (Cockcroft/Gault) \> 30 mL/min/1.73 m\^2 * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN (or \< 5 x ULN for subjects with lymphomatous infiltration of the liver) * Total bilirubin =\< 2 (or \< 3.0 for subjects with Gilbert's syndrome or lymphomatous infiltration of the liver) * Common Terminology Criteria for Adverse Events (CTCAE) Grade =\< 1 dyspnea * Saturation of oxygen (Sa02) \>= 92% on room air * Patients with clinically significant pulmonary dysfunction, as determined by medical history and physical exam should undergo pulmonary function testing and must have a forced expiratory volume in 1 second (FEV1) of \>= 50% of predicted value * Patients with clinically significant pulmonary dysfunction, as determined by medical history and physical exam should undergo pulmonary function testing and must have a diffusing capacity of the lung for carbon monoxide (DLCO; corrected) \>= 40% of predicted value * Left ventricular ejection fraction (LVEF) \>= 40% as assessed by echocardiogram or multiple uptake gated acquisition (MUGA) * Patients with Fridericia's corrected QT interval (QTcF) \> 450 ms for men and \> 470 ms for women will require clearance by a cardiologist * Women of reproductive potential (defined as all women physiologically capable of becoming pregnant) must agree to use suitable methods of contraception for 1 month after the last dose of study therapy (NKTR-255) * Males who have partners of reproductive potential must agree to use an effective barrier contraceptive method for 1 month after the last dose of study therapy (NKTR-255) * Ability to understand and provide informed consent * Able and willing to comply with study visit schedule and procedures, including tumor biopsy where feasible and with acceptable risk Exclusion Criteria: * Planned use of therapeutic doses of corticosteroids (\> 20 mg/day prednisone or equivalent) or other systemic immunosuppression within 7 days prior to leukapheresis or within 72 hours prior to liso-cel infusion. Topical and/or inhaled steroids are permitted * Prior treatment with any CD19 CAR-T cell therapy * For allogeneic hematopoietic cell transplant (HCT) recipients, active graft versus host disease (GVHD) and/or systemic GVHD therapy within 30 days prior to planned leukapheresis * Known active hepatitis B (detectable hepatitis B deoxyribonucleic acid \[DNA\]) or hepatitis C (detectable hepatitis C ribonucleic acid \[RNA\]) * Known human immunodeficiency virus (HIV) infection * Pregnant or breastfeeding women * Prior treatment with any IL-2 or IL-15 agonist and/or biosimilar agents * Active autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., ulcerative colitis, Crohn's disease\], celiac disease, or other serious chronic gastrointestinal conditions associated with diarrhea, autoimmune vasculitis, systemic lupus erythematosus, Wegener syndrome \[granulomatosis with polyangiitis\], myasthenia gravis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc.) requiring immunosuppressive therapy. The following are exceptions to this criterion: * Vitiligo. * Alopecia. * Hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement. * Type 1 diabetes mellitus. * Psoriasis not requiring systemic treatment. * Conditions considered to be low risk of serious deterioration by the principal investigator (PI). * History of any one of the following cardiovascular conditions within the past 6 months: class III or IV heart failure as defined by the New York Heart Association (NYHA), cardiac angioplasty or stenting, myocardial infarction, or unstable angina; unless clearance by a cardiologist is obtained. History of other clinically significant cardiac disease that, in the opinion of the PI or designee, is a contraindication to study treatment is also excluded * History or presence of clinically relevant central nervous system (CNS) pathology, such as epilepsy, seizure, paresis, aphasia, stroke, severe brain injuries, dementia, Parkinson's disease, cerebellar disease, or psychosis that in the opinion of the PI is a contraindication to study treatment. * Patients with active parenchymal CNS involvement by malignancy will be excluded. Patients with prior or current secondary leptomeningeal CNS disease are eligible. CNS disease prophylaxis must be stopped at least 1 week prior to liso-cel infusion * History of solid organ transplantation * Active, serious, and uncontrolled infection(s)