The goal of this clinical research study is to find the highest tolerable dose of belinostat that can be given in combination with azacitidine, gemcitabine, busulfan, and melphalan to patients who are scheduled to have a stem cell transplant. If you have diffuse large B-cell lymphoma (DLBCL), you will also receive rituximab. Researchers also want to learn about the safety and effectiveness of this combination.