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

PRIMARY OBJECTIVE: I. To assess the increase in CD27+/CD28+ T cells, after 8 to 15 day exposure duvelisib prior to collection of mononuclear cells for chimeric antigen receptor T-cell (CART cell) manufacturing. SECONDARY OBJECTIVES: I. To evaluate patient compliance with duvelisib. II. To evaluate the time required for manufacturing CAR-T using mononuclear cells from duvelisib-treated patients. III. To describe the frequencies of CD27/28 double positive T cells and CD4/8 double negative T cells. IV. To evaluate expansion and persistence of CAR-T cells V. To evaluate overall response rates following CAR-T cell therapy VI.To evaluate survival rates following CAR-T cell therapy VII. To describe the frequency of CRS and neurotoxicity requiring ICU transfer (for CRS or neurotoxicity) and/or treatment VIII. Describe the safety and tolerability profile of duvelisib OUTLINE: Patients receive duvelisib orally (PO) twice daily (BID) for 2 weeks prior to collection of CAR-T cells in the absence of disease progression or unacceptable toxicity. Patients then receive tisagenlecleucel via infusion. Patients are followed up 100 days after CAR-T infusion.