Duvelisib Exposure to Enhance Immune Profiles of T Cells in Patients With Recurrent or Refractory Diffuse Large B-Cell Lymphoma, DEEP T CELLS Study

Inclusion Criteria:

* Patients must have a biopsy proven diagnosis of relapsed/refractory diffuse large B-cell lymphoma (DLBCL)
* Eastern Cooperative Oncology Group (ECOG) \< 2
* Serum creatinine (Cr) \< 2.0 mg/dL
* Alanine aminotransferase (AST)/aspartate aminotransferase (ALT) \< 2 x upper limit of normal (ULN)
* Total bilirubin \< 2.0 mg/dL
* Hemoglobin \> 8 g/dL
* Platelet count \> 50 K/mcl
* An absolute neutrophil count (ANC) \> 1,000/mm\^3
* An absolute lymphocyte count (ALC) \> 300/mm\^3
* Completion of all previous therapy (including surgery, radiotherapy, chemotherapy, immunotherapy, or investigational therapy) for the treatment of their DLBCL \>= 2 weeks before the start of duvelisib. There is no limit on how many previous lines of treatment a patient may have received
* The effects of duvelisib on the developing human fetus are unknown. For this reason, women of child-bearing potential (WOCBP) must have a negative serum or urine pregnancy test prior to starting therapy. WOCBP and men must agree to use highly effective contraception (hormonal or barrier method of birth control; abstinence) from enrollment into this study until at least 12 months after tisagenlecleucel infusion and until CAR-T cells are no longer present by quantitative polymerase chain reaction (qPCR) on two consecutive tests (qPCR tests will be available upon request). A woman of childbearing potential (WOCBP) is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use highly effective contraception prior to the study, for the duration of study participation, and 3 months after completion of duvelisib administration. WOCBP must have a negative pregnancy test within 24 hours of leukapheresis, lymphodepletion (if performed) and tisagenlecleucel infusion (if lymphodepletion not performed)
* The patient must be willing to comply with fertility requirements as below:
* Total abstinence (when this is in line with the usual practice and lifestyle of the patient). Periodic abstinence (i.e, calendar, ovulation, post-ovulation methods) and withdrawals are not acceptable forms of contraception
* Female sterilization (have had surgical bilateral oophorectomy with or without a hysterectomy), total hysterectomy or bilateral tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow-up hormone assessment
* Male sterilization (at least 6 months prior to screening). For female patients on the study, the vasectomized male partner should be the sole partner
* Use of oral (estrogen and progesterone), injected or implanted hormonal methods of contraception, or placement of an intrauterine device (IUD) or intrauterine system (IUS) or other forms of contraception that comparable efficacy (failure rate \< 1%). In case of oral contraception, the woman should be stable on the same pill for a minimum of 3 months prior to enrollment on the study
* Sexually active males must use a condom during intercourse from enrollment into this study until at least 12 months after tisagenlecleucel infusion and until CAR-T cells are no longer present by qPCR on two consecutive tests (qPCR tests will be available upon request). A condom is required of all sexually active male patients to prevent them from fathering a child AND to prevent delivery of study treatment via seminal fluid to their partner
* Female patients must be either postmenopausal, free from menses \>= 2 years (yrs), surgically sterilized, willing to use two adequate barrier methods of contraception to prevent pregnancy or agree to abstain from heterosexual activity starting with screening and for 5 months after last treatment in all patients
* Patients must agree not to donate blood, sperm/ova or any other organs while taking protocol therapy and for at least 12 months after stopping treatment
* Willingness and ability of the patient to comply with scheduled visits, drug administration plan, protocol specified laboratory tests, other study procedures and study restrictions
* Evidence of personally signed informed consent indicating that the subject is aware of the neoplastic nature of the disease and has been informed on the procedures to be followed, the experimental nature of the therapy, alternative, potential risks and discomforts, potential benefits and other pertinent aspects of study participation

Exclusion Criteria:

* Primary central nervous system lymphoma
* Patients with central nervous system (CNS) involvement of lymphoma
* History of autoimmune disease, including but not limited to:

  * Inflammatory bowel diseases (Crohn's disease, ulcerative colitis, celiac disease)
  * Systemic lupus erythematosus
  * Grave's disease
  * Myasthenia gravis
  * Rheumatoid arthritis
  * Wegner's syndrome
* Patients with history of drug reaction and eosinophilia systemic syndrome (DRESS) or toxic epidermal necrolysis (TEN)
* History of human immunodeficiency virus (HIV), active Hepatitis C Infection or active Hepatitis B infection as defined by:

  * Patients with a positive hepatitis B surface antigen (HBsAg) or hepatitis C antibody (HCV Ab) will be excluded
  * Patients with a positive hepatitis B core antibody (HBcAb) must have negative hepatitis B virus (HBV) deoxyribonucleic acid (DNA) to be eligible and must be periodically monitored for HBV reactivation by institutional guidelines
* Patients with known active cytomegalovirus (CMV) or Epstein-Barr virus (EBV) infection (i.e., subjects with detectable viral load)
* Patients with ongoing treatment for systemic bacterial, fungal or viral infection
* Patients with history of immune or drug mediated colitis, hepatitis or pneumonitis
* Patients with previous treatment with a PI3K inhibitor
* Patients currently on immunosuppressive therapy, including steroids
* Previous CD 19 directed therapy
* Patients who have had chemotherapy or radiotherapy within 2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 2 weeks earlier (i.e., have residual toxicities \> grade 1)
* Patients receiving any other investigational drugs
* Pregnant women are excluded from this study because duvelisib is agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with duvelisib, breastfeeding should be discontinued if the mother is treated with duvelisib and breastfeeding should not be resumed until at least 1 month after last dose of duvelisib
* Patients with history of chronic liver disease or veno-occlusive disease
* Patients that are unable to receive prophylactic treatment for pneumocystis, herpes simplex virus (HSV), or herpes zoster "(VZV) at screening
* Patients with history of tuberculosis treatment within the 2 years prior to randomization
* Patients with prior surgery or gastrointestinal dysfunction that may affect drug absorption (e.g., gastric bypass surgery, gastrectomy). Subjects with clinically significant medical condition of malabsorption, inflammatory bowel disease, chronic conditions which manifest with diarrhea, refractory nausea, vomiting or any other condition that will interfere significantly with drug absorption
* Concurrent administration of medications or foods that are strong inhibitors or inducers of cytochrome P450 3A (CYP3A). No prior use within 2 weeks before the start of study intervention
* Administration of a live or live attenuated vaccine within 6 weeks of randomization