• Histologically confirmed B-cell non-Hodgkin's lymphoma:

• DLBCL DLBCL or associated subtype, defined by WHO 2016 classification:

• DLBCL not otherwise specified (NOS)

• High-grade B cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements

• High-grade B cell lymphoma (NOS)

• Primary mediastinal (thymic) large B cell lymphoma

• Transformed lymphoma (e.g., transformed follicular, or marginal zone lymphoma, follicular lymphoma (FL Grade 3)

• CNS Cohort only: B-cell primary or secondary central nervous system lymphoma (PCNSL or SCNSL)

• Mantle Cell Lymphoma (MCL) Cohort: Histologically confirmed MCL determined by overexpression of cyclin D1 or presence of t(11;14) (q13; q32) translocation

• Richter's Transformation (RT) Cohort: Histologically confirmed Richter's transformation (RT) to a diffuse large B-cell lymphoma (DLBCL) subtype from underlying CLL (clonally related)

• Relapsed or refractory disease is defined for DLBCL (and associated subtypes) population as failure of 2 or more lines of chemotherapy including rituximab or equivalent and anthracycline and either having failed autologous stem cell transplant (ASCT), or ineligible, not intended for or not consenting to ASCT

• Chemotherapy-refractory disease is defined as persistent disease after last line of therapy or relapsed or persistent disease after prior ASCT for lymphoma

• Disease relapse in subjects without prior ASCT is defined as relapse of disease after the last dose of most recent therapy regimen

• CNS Cohort: Subjects with relapsed/refractory PCNSL that have failed (or unable to tolerate) at least first-line therapy.

• No contraindications for MRI evaluation

• CNS Cohort: Subjects with SCNSL must have relapsed or refractory disease after having received at least one prior line of systemic therapy

• Prior lines of systemic therapy should include an anti-CD20 monoclonal antibody and anthracycline containing chemotherapy regimen and/or with or without an autologous stem cell transplant

• No contraindications for MRI evaluation

• MCL Cohort: Subjects with relapsed/refractory disease after at least one prior systemic treatment, that must include:

• Cytotoxic rituximab-based chemotherapy regimen (eg, rituximab bendamustine, R-CHOP, R-DHAP, R-ARA-C) AND

• BTK inhibitor

• RT Cohort: Subject must have relapsed/refractory disease after at least one prior systemic treatment following Richter's Transformation

• Age ≥18 years

• Eastern Cooperative Oncology Group (ECOG) performance status that is either 0 or 1 at screening. ECOG performance status of 2 at screen is allowed if the decrease in performance status is due to lymphoma

• Measurable disease according to Lugano 2014 criteria for assessing FDG-PET/CT in systemic lymphoma (Cheson et al, 2014). Measurable disease according to IPCG criteria will be assessed by brain/spine MRI for CNS disease

• Subject must have a tumor biopsy sample (at least 16 unstained slides of tissue or tissue block) from the most recent relapse available prior to MB-CART2019.1 infusion. If medically not feasible to obtain a biopsy from the most recent relapse and for cases when the amount of tissue is limited, the sponsor should be consulted, to confirm adequacy of the sample for study required analyses

• No clinical suspicion of central nervous system (CNS) lymphoma (not applicable to CNS cohort)

• If the subject has history of CNS disease (not applicable to CNS cohort), then he/she must have no signs or symptoms of CNS disease, have no active disease on magnetic resonance imaging (MRI), have no large cell lymphoma present in cerebral spinal fluid (CSF), regardless of the number of white blood cells (WBCs)

• If has history of cerebral vascular accident (CVA), the CVA event must be greater than 12 months prior to leukapheresis. Any neurological deficits must be stable

• A creatinine clearance (as estimated by direct urine collection or Cockcroft-Gault Equation) \> 45mL/min

• Cardiac ejection fraction (EF) ≥ 45% as determined by an echocardiogram (ECHO) or Multigated Radionuclide Angiography (MUGA)

• Resting O2 saturation \>90% on room air

• Serum alanine aminotransferase (ALT) / aspartate aminotransferase (AST)\<5 times the Upper Limit of Normal (ULN) for age

• Total bilirubin \<1.5 mg/dl, except in individuals with Gilbert's syndrome

• Absolute neutrophil count (ANC) \> 1000/μL

• Absolute lymphocyte count \> 100/μL

• Platelet count \> 50,000/µL

• Estimated life expectancy of more than 3 months other than primary disease