Safety and Tolerability of Myeloablative Conditioning and Autologous Stem Cell Transplantation Followed by Polatuzumab Vedotin (PV) Immunoconjugate Therapy in Patients With B-cell Non-Hodgkin and Hodgkin Lymphoma

Inclusion Criteria: * Diagnosis B-cell NHL: Burkitt lymphoma, Diffuse Large B Cell Lymphoma, Follicular Lymphoma, Mantle Cell Lymphoma, Marginal Zone Lymphoma, Transformed Follicular Lymphoma, Richter syndrome, and CD20+ Hodgkin Lymphoma. * Disease Status Primary Induction Failure, 1st, 2nd or 3rd relapse/progression having attained a CR, PR, or stable disease post reinduction therapy. * Performance Level Patients must have a performance status ≥ 50%. Use Karnofsky for patients \> 16 years of age and Lansky for patients less than or equal to 16 years of age. See Appendix I for performance score. * Life Expectancy Patients must have a life expectancy of \> 6 weeks. * Prior Therapy Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study. 1. Myelosuppressive chemotherapy: Must not have received within 2 weeks of entry onto this study (4 weeks if prior nitrosourea). 2. Biologic (anti-neoplastic agent): At least 7 days since the completion of therapy with a biologic agent. * Organ Function Requirements Adequate Renal Function Defined As: * Creatinine clearance or radioisotope GFR \> 60 mL/min/1.73 m2 or * A serum creatinine based on age/gender as follows: Age Maximum Serum Creatinine (mg/dL) Male Female * 12 to \< 13 years 1.2 1.2 13 to \< 16 years 1.5 1.4 * 16 years 1.7 1.4 * Adequate Liver Function Defined As: * Total bilirubin less than or equal to 1.5 x upper limit of normal (ULN) for age, and * SGOT (AST) or SGPT (ALT) \< 3 x upper limit of normal (ULN) for age for presumed hepatic leukemia or lymphoma. * Adequate Cardiac Function Defined As: * Shortening fraction of \> 27% by echocardiogram, or * Ejection fraction of \> 50% by radionuclide angiogram. * Adequate Pulmonary Function Defined As: • Normal respiratory rate for age and a pulse oximetry \> 94% on room air unless due to underlying malignancy. * Peripheral Blood Stem Cell Collection • Patients have a target of 5.0 x 106 CD34 (minimum of 2.5 x 106 CD34) PBSC collected and cryopreserved prior to start of myeloablative conditioning * All patients and/or their parents or legal guardians must sign a written informed consent. Exclusion Criteria: * Patient may not have had a prior stem cell transplant * Patients must not have active CNS lymphoma * Other concurrent investigational agents for treatment of B-cell lymphoma * Pregnancy and/or active Breast Feeding * Sexually active patients of reproductive potential are not eligible unless they have agreed to use an effective contraceptive method for the duration of their study participation. * Patient must not have an uncontrolled infection. * Patient must not have ≥ Grade 3 neuropathy.