This is an investigational study. Belinostat, busulfan, and rituximab are FDA approved and commercially available for the treatment of lymphoma. Gemcitabine is FDA approved and commercially available for the treatment of breast cancer, non-small cell lung cancer (NSCLC), ovarian cancer, and pancreatic cancer. Melphalan is FDA approved and commercially available for the treatment of multiple myeloma (MM). Azacitidine is FDA approved and commercially available for the treatment of myelodysplastic syndrome (MDS). The use of these study drugs in combination to treat lymphoma is considered investigational.