Venetoclax, Carmustine, Etoposide, Cytarabine, and Melphalan Before Stem Cell Transplant in Treating Participants With Relapsed or Refractory Non-Hodgkin Lymphoma

Inclusion Criteria: * Subjects must have histologically confirmed diagnosis of non-Hodgkin?s lymphoma that has relapsed, or is refractory, after upfront induction therapy. Excluded histologies are T-cell lymphomas, post-transplant lymphoproliferative disorder, Burkitt lymphoma, lymphoblastic lymphoma, chronic lymphocytic leukemia/small lymphocytic lymphoma. All other histologies are eligible that include but not limited to: diffuse-large B-cell lymphoma, follicular lymphoma (grades I, II, and III), marginal zone lymphoma, transformed indolent lymphoma, grey zone lymphoma, and undifferentiated B-cell lymphoma. Patients with non-Hodgkin's lymphoma (NHL) who are at high risk of relapse can be enrolled in sustained partial response (PR) after induction chemotherapy (PR1) * Expected survival of more than six months * Karnofsky performance status \>= 80% * Within 1 week prior to initiation of treatment: Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) \< 3 x upper limits of normal (ULN) unless due to disease * Within 1 week prior to initiation of treatment: Total bilirubin \< 2 x ULN unless due to disease * Within 1 week prior to initiation of treatment: Calculated glomerular filtration rate (GFR) 30 ml/min * Within 1 week prior to initiation of treatment: Absolute neutrophil count (ANC) \> 500 cells/mm\^3 * Within 1 week prior to initiation of treatment: Platelet count \> 50 mm\^3 * Left ventricular ejection fraction \>= 40% * Diffusion capacity of carbon monoxide …