AutologousCD22 Chimeric Antigen Receptor (CAR)T Cells in w/Recurrent/Refractory B Cell Lymphomas

Inclusion Criteria: * Disease: Must have histologically confirmed disease as defined by WHO 2016\[117\] of one of the following: Follicular Lymphoma, grade 1-3a 1. Relapsed or refractory disease after at least 2 lines of systemic therapy. Prior therapy must have included an anti-CD20 monoclonal antibody combined with systemic therapy (single-agent anti- CD20 antibody does not count as line of therapy for eligibility nor does local radiation). Anti-CD20 antibody is not required for participants with CD20 negative disease. A systemic therapy includes, but is not limited to: Bendamustine, CHOP, CVP, CART therapy, lenalidomide, or platinum-based chemotherapy. 2. Relapsed or progressive disease within 24 months of initiation of the initial course of chemotherapy (also known as progression of disease within 24 months POD24). Initial treatment must have included an anti-CD20 monoclonal antibody (unless CD20 negative) plus either Bendamustine, CHOP or CVP (R-Chemo). Must have completed 3 or more cycles of R-Chemo. Progression is measured from the initial day of treatment of the first cycle of R-Chemo. In the case of those who received anti-CD20 monoclonal antibody monotherapy previously and then received R-Chemo are also eligible if they are POD24, and progression is measured from the initial day of treatment of the first cycle of R-Chemo and not from the initial day of anti-CD20 monoclonal antibody monotherapy. Mantle Cell Lymphoma 1. Relapsed or refractory disease after at least 2 lines of systemic therapy. Prior therapy must have included an anti-CD20 monoclonal antibody combined with systemic therapy. Anti-CD20 antibody is not required for participants with CD20negative disease. 2\. Participants who have received an anti-CD20 monoclonal antibody in combination with chemotherapy AND a Bruton's Tyrosine Kinase inhibitor as a single line of therapy are also eligible. Hairy cell leukemia (HCL) 1. Diagnosis of HCL and require treatment as defined by having HCL-related anemia (hemoglobin \<11 g/dL), thrombocytopenia (platelets\<100 x 10\^9 /L), or neutropenia (absolute neutrophil count below 1.5 x 10\^9/L); symptomatic splenomegaly or adenopathy; or other constitutional symptoms directly related to HCL; 2. Must have progressed or been refractory to 2 lines of therapy including a purine nucleoside analog. Lymphoplasmacytic lymphoma (Waldenstrom macroglobulinemia (WM)) - participants must meet all eligibility criteria listed 1\. Must have confirmed diagnosis of WM based on Second International Workshop on WM 2. Relapsed or refractory disease after 2 or more lines of therapy 1\. Prior therapies must include a i. BTKi ii. either chemotherapy and/or proteasome inhibitor 3. Requires treatment based on the recommendations from the Second International Workshop on WM 4. Requires the presence of serum IgM that is at least 2 times the upper limit of normal 5. Patients cannot require plasmapheresis for symptomatic hyperviscosity. 6. Patients cannot have symptomatic central nervous system involvement (Bing-Neel syndrome) that would prevent the assessment of neurotoxicity 7. Patients cannot have transformed to large B cell lymphoma Burkitt lymphoma (BL) 1\. Relapsed or refractory to front line chemoimmunotherapy; Participants with high-grade B-cell lymphoma with MYC and BCL2 and/orBCL6 rearrangements will be excluded. Marginal zone lymphoma (MZL) 1\. Must have received 2 prior lines of therapy including rituximab in combination with chemotherapy or a BTKi Histologically confirmed Large B-cell lymphoma (LBCL) by WHO 2008 including: i. DLBCL not otherwise specified; DLBCL associated with chronic inflammation; Epstein Barr virus (EBV)+ DLBCL of the elderly; OR ii. primary mediastinal (thymic) large B cell lymphoma; OR iii. transformation of follicular lymphoma, marginal zone lymphoma or chronic lymphocytic leukemia/small lymphocytic lymphoma to DLBCL; OR iv. Follicular Lymphoma Grade 3B • Subjects with DLBCL, Follicular Lymphoma Grade 3B -or- Subjects with transformed FL and MZL who HAVE NOT received chemotherapy prior to transformation: 1\) Must have received an anthracycline regimen and an anti CD20 monoclonal antibody (unless documented CD20-negative) and be refractory or relapsed after second line of LBCL treatment. Subjects with a partial response to second line therapy must be ineligible for autologous transplant. * Subjects with transformed FL and MZL who HAVE received anthracycline-containing chemotherapy prior to transformation must have progressed, had SD or recurred with transformed disease after initial treatment for LBCL: 1. Must have progressed, had SD, or recurred with transformed disease after initial treatment for LBCL Note: T cell/histiocyte rich large B cell lymphoma is not eligible The following criteria apply to all participants unless otherwise noted: 2\. Measurable Disease: 1. a. Participants with Follicular Lymphoma, Mantle Cell Lymphoma, Burkitt Lymphoma and Marginal Zone Lymphoma must have measurable disease according to the revised IWG Response Criteria for Malignant Lymphoma. Lesions that have been previously irradiated will be considered measurable only if progression has been documented following completion of radiation therapy. b. If participants with Follicular Lymphoma, Mantle Cell Lymphoma, Burkitt Lymphoma, Marginal Zone Lymphoma, and Large B cell Lymphoma that do not have measurable disease according to the revised IWG Response Criteria for Malignant Lymphoma, but have disease that is greater than 2% of events by flow cytometry in the peripheral blood or bone marrow will be eligible 2. c. Participants with Hairy Cell Lymphoma must have presence of leukemic cells in the bone marrow or blood stream. 3. d. Participants with Lymphoplasmacytic lymphoma must have the presence of serum IgM that is at least 2 times the upper limit of normal. 3\. CD22 expression, at any level: Participants must have archival tissue available for analys