The goal of this clinical research study is to find the highest tolerable dose of azacitidine that can be given with vorinostat, gemcitabine, busulfan, and melphalan, with a stem cell transplant, and with or without rituximab. Researchers also want to learn about the safety and level of effectiveness of this combination.

Study Groups:

If you have been found to be eligible to take part in this study and you agree, you will be assigned to a dose level of azacitidine based on when you join this study. Up to 7 dose levels of azacitidine will be tested. At least 3 participants will be enrolled at each dose level. The first group of participants will receive the lowest dose level. Each new group will receive a higher dose than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of azacitidine is found.

All participants will receive the same dose level of vorinostat, gemcitabine, busulfan, and melphalan, and all patients with B-cell cancer will receive the same dose of rituximab. However, if the first group has bad side effects, the dose level of gemcitabine may be lowered for all other groups.

Busulfan Test Dose:

You will receive a test dose of busulfan by vein over about 60 minutes. This low-level test dose of busulfan is to check how the level of busulfan in your blood levels changes over time. This information will be used to decide the next dose needed to reach the target blood level that matches your body size. You will most likely receive this as an outpatient during the week before you are admitted to the hospital. If it cannot be given as an outpatient, you will be admitted to the hospital on Day -12 (12 days before your stem cells are returned to your body) and the test dose will be given on Day -11.

About 11 samples of blood (about 1 teaspoon each time) will be drawn for pharmacokinetic (PK) testing of busulfan. PK testing measures the amount of study drug in the body at different time points and will help the study doctor determine what your dose of busulfan should be on study. These blood samples will be drawn at various timepoints before you receive busulfan and over about the next 11 hours. The blood samples will be repeated again on the first day of high-dose busulfan treatment (Day -8). A temporary heparin lock line will be placed in your vein to lower the number of needle sticks needed for these draws. If it is not possible for the PK tests to be performed for technical or scheduling reasons, you will receive the standard fixed dose of busulfan.

On Days -14, -13, and -12, you will receive palifermin by vein over about 30 seconds each day to help decrease the risk of side effects in the mouth and throat.

Study Drug Administration (for all patients):

In stem cell transplants, the days before you receive your stem cells are called minus days. The day you receive the stem cells is called Day 0. The days after you receive your stem cells are called plus days.

Beginning on Day -9, you will swish the liquids caphosol and glutamine in your mouth 4 times a day, for about 2 minutes each time. You will swish these liquids every day until you leave the hospital. You will swallow the glutamine. These drugs are used to help decrease the risk of side effects in the mouth and throat.

On Day -11 through Day -2, you will take vorinostat by mouth, with food. One hour later each day, you will receive azacitidine by vein over 1 hour. You will receive dexamethasone by vein 2 times each day.

If you have a B-cell cancer, you will receive rituximab (a treatment used for certain lymphomas) by vein over 3-6 hours as part of standard of care, on Day -9.

On Day -8, you will receive gemcitabine by vein over 4 ½ hours.

On Days -8, -7, -6, and -5, you will receive busulfan by vein over 2 hours.

On Day -3, you will receive gemcitabine by vein over 4 ½ hours and then melphalan by vein over 30 minutes.

On Day -2, you will receive melphalan by vein over 30 minutes.

On Day -1, you will rest (you will not receive chemotherapy).

On Day 0, you will receive your stem cells by vein over about 30-60 minutes.

You will receive 3 more doses of palifermin by vein over 15-30 seconds on Days 0, +1, and +2.

As part of standard care, you will receive G-CSF (filgrastim) as an injection just under your skin 1 time each day starting on Day +5 until your blood cell levels return to normal.

Study Tests:

About 100 days after the transplant:

• You will have a physical exam.
• Blood (about 4 teaspoons) and urine will be collected for routine tests.
• If the doctor thinks it is needed, you may have a bone marrow aspiration and biopsy to check the status of the disease. To collect a bone marrow aspiration/biopsy, an area of the hip is numbed with anesthetic, and a small amount of bone marrow and bone is withdrawn through a large needle.

Length of Study:

As part of standard care, you will remain in the hospital for about 3-4 weeks after the transplant. After you are released from the hospital, you will continue as an outpatient in the Houston area to be monitored for infections and transplant-related complications.

You will be taken off study about 100 days after the transplant. You may be taken off study early if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions.

This is an investigational study. Azacitidine, vorinostat, gemcitabine, busulfan, melphalan, and rituximab are all FDA approved and commercially available. The use of these study drugs in combination is investigational.

Up to 60 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Age 15 to 65 years.
2. Patients with Hodgkin's lymphoma with one or more of the following: a) Less than complete response to first-line chemotherapy. b) Relapse within 12 months of completion of first-line chemotherapy. c) Relapse within a prior irradiation field. d) Less than complete metabolic response to second-line chemotherapy. e) Second relapse or beyond. f) Extranodal disease at the time of relapse. g) Presence of B symptoms at the time of persistent disease upon completion of first-line chemotherapy, relapse or progressive disease. h) Bulky disease (defined as any lesion greater than 5 cm) at the time of persistent disease upon completion of first-line chemotherapy, relapse or progressive disease.
3. Patients with non-Hodgkin's lymphoma and one or more of the following: 1. Diffuse large B-cell lymphoma with one or more of the following: a) Primary refractory disease. b) Relapse within 12 months of completion of first-line therapy. c) Secondary IPI >1. d) Less than PR to first-line salvage chemotherapy. e) Kinetic failure after salvage chemotherapy; f) Prior treatment with 3 or more lines of therapy. g) Patients with double-hit or triple-hit NHL, in any state of the disease. 2. Peripheral T-cell lymphoma not otherwise specified (PTCL-NOS) in any stage of the disease. 3. Angioimmunoblastic T-cell lymphoma (AITL) in any stage of the disease. 4. Refractory or recurrent Burkitt¹s lymphoma. 5. Any other lymphoma that is refractory or relapsed and that does not qualify for treatment protocols of higher priority.
4. Adequate renal function, as defined by estimated serum creatinine clearance >/=50 ml/min (MDRD method from National Kidney Disease Education Program, NKDEP) and/or serum creatinine </= 1.8 mg/dL.
5. Adequate hepatic function, as defined by SGOT and/or SGPT </= 3 x upper limit of normal; serum bilirubin and alkaline phosphatase </= 2 x upper limit of normal.
6. Adequate pulmonary function with FEV1, FVC and DLCO >/= 50% of expected corrected for hemoglobin.
7. Adequate cardiac function with left ventricular ejection fraction >/= 40%. No uncontrolled arrhythmias or symptomatic cardiac disease.
8. Zubrod performance status <2.
9. Negative Beta HCG text in a woman with child-bearing potential, defined as not post-menopausal for 12 months or no previous surgical sterilization.

Exclusion Criteria:

1. Patients with grade >/= 3 non-hematologic toxicity from previous therapy that has not resolved to </= grade 1.
2. Patients with prior whole brain irradiation.
3. Patients with active hepatitis B, either active carrier (HBsAg +) or viremic (HBV DNA >/=10,000 copies/mL, or >/= 2,000 IU/mL).
4. Evidence of either cirrhosis or stage 3-4 liver fibrosis in patients with chronic hepatitis C or positive hepatitis C serology.
5. Patients with active inflammatory bowel disease.
6. Active infection requiring parenteral antibiotics.
7. HIV infection, unless the patient is receiving effective antiretroviral therapy with undetectable viral load and normal CD4 counts.
8. Patients having received radiation therapy in the month prior to enrollment.

Up to 100 Days post autologous transplant.