Study Evaluating UCART20x22 in B-Cell Non-Hodgkin Lymphoma (NatHaLi-01)

Inclusion Criteria: Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 Relapsed or refractory (R/R) mature B-NHL per 2016 WHO criteria and positive for CD20 and/or CD22 Subjects with NHL subtypes defined by WHO: -Dose-Finding Part: R/R mature B-NHL (except chronic lymphocytic leukemia/small lymphocytic leukemia [CLL/SLL], Richter's transformation from prior CLL/SLL, Burkitt's lymphoma, and Waldenstrom's macroglobulinemia) -Dose-Expansion Part: R/R LBCL, defined as: i. DLBCL; ii. High-grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements; iii. Transformed FL or transformed marginal zone lymphoma (MZL); iv. Follicular lymphoma Grade 3B R/R disease after at least 2 lines of prior treatment, which must have included: -An Anti-CD20 MoAb and an anthracycline for DLBCL, high-grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements, primary mediastinal large B-cell lymphoma (PMBCL), or transformed FL or MZL -An alkylating agent in combination with an anti-CD20 MoAb for FL -An anthracycline or bendamustine-containing chemotherapy regimen and a Bruton's tyrosine kinase (BTK) inhibitor for mantle cell lymphoma (MCL) -Autologous anti-CD19 CAR T-cell therapy, if approved and available for the indicated lymphoma subtype, unless the subject is unable or is ineligible to receive approved autologous anti-CD19 CAR T-cell therapy (e.g., fail leukapheresis or manufacture, unable to wait for manufacture, CD19 negative disease, etc.) Exclusion Criteria: Prior use of an investigational product (except for cell or gene therapies and MoAbs) within 5 half-lives or within 14 days, whichever is shorter, prior to start of LD regimen Previous approved therapy including chemotherapy, biologic (except MoAbs), or targeted therapy for R/R B-NHL with 5 half-lives or within 14 days, whichever is shorter, prior to start of the LD regimen Prior MoAb therapy (approved or investigational) within 30 days prior to start of LD Prior systemic immunostimulatory agent within 3 half-lives prior to start of the LD regimen Prior cell or gene therapy (approved or investigational) within 6 weeks of the start of LD Prior cell or gene therapy (approved or investigational) targeting both CD20 and CD22 Autologous HSCT infusion within 6 weeks of the start of LD Allogeneic HSCT within 3 months of the start of LD, or donor lymphocyte infusion within 6 weeks of the start of LD Subjects should be off all immunosuppressive therapies for at least 6 weeks prior to start of LD Radiotherapy within 8 weeks (except for palliative radiotherapy for specific on-target lesions) (prior to start of LD regimen) Active acute or chronic graft versus host disease Evidence of active central nervous system (CNS) lymphoma or previous CNS involvement of R/R B-NHL Presence of an active and clinically relevant CNS disorder Daily treatment with >20 mg prednisone or equivalent Known active infection, or reactivation of a latent infection, whether bacterial or viral, fungal, mycobacterial, or other pathogens History of hypersensitivity to alemtuzumab History of neutralizing anti-drug antibody against alemtuzumab Any known uncontrolled cardiovascular disease within 3 months of enrollment Subjects requiring immunosuppressive treatment Major surgery within 28 days prior to start of LD Evidence of another uncontrolled malignancy within 2 years prior to Screening (except in situ nonmelanoma skin cell cancers and/or carcinoma in-situ of the cervix)