Dose-escalation and Dose-expansion Study of Safety of Azer-cel (PBCAR0191) in Participants With Relapsed/Refractory (r/r) Non-Hodgkin Lymphoma (NHL) and r/r B-cell Acute Lymphoblastic Leukemia (B-ALL)

Key Inclusion Criteria Criteria for B-ALL: • Participant has confirmed unequivocal r/r CD19+ B-ALL. Criteria for NHL and CLL/SLL: • Participant has unequivocal aggressive CD19+ r/r B-cell NHL that is confirmed by tumor biopsy tissue from last relapse after CD19-directed therapy. For Phase 1 Dose Escalation: * Diffuse large B-cell lymphoma (DLBCL) including Richter's transformation * Follicular lymphoma (FL) including Grade 3 or transformed FL * High-grade B-cell lymphoma (HGBCL) * Primary mediastinal lymphoma For Phase 1b Dose Expansion (CAR T-relapsed cohort): * DLBCL not otherwise specified (NOS) * HGBCL * DLBCL transformed from the following indolent lymphoma subtypes (FL, Marginal Zone lymphoma \[MZL\], and Waldenstrom's Macroglobulinemia \[WM\]) * Other large B-cell lymphoma (LBCL) subtypes may be enrolled with approval from the Medical Monitor. * Participants previously treated with CD19-directed autologous CAR T therapies have received no more than 2 lines of therapy after administration of their previous CAR T product. * For the expansion CAR T-relapsed cohort only: Participants must have received autologous CD19-directed CAR T therapy and demonstrated clinical response to the treatment at Day 28 or later, followed by relapse or progression. For Phase 1b dose expansion (CAR T-naive cohort): * DLBCL NOS * DLBCL transformed from the following indolent lymphoma subtypes (FL, MZL, and WM) * HGBCL * FL (Grade 1-3a) * MZL that is fluorodeoxyglucose (FDG)-avid on p…