The goal of this clinical research study is to learn if giving romidepsin before and after a stem cell transplant in combination with fludarabine and busulfan can help to control leukemia or lymphoma. Researchers also want to learn the highest tolerable dose of romidepsin that can be given with this combination.

The safety of this combination and the safety of giving romidepsin after a stem cell transplant will also be studied.

This is an investigational study. Romidepsin is FDA approved and commercially available for the treatment of CTCL in patients who have received at least 1 systemic (affecting the whole body) therapy before. Busulfan and fludarabine are FDA approved and commercially available for use with a stem cell transplant.

The use of the combination of romidepsin, busulfan, and fludarabine to treat the type of leukemia or lymphoma you have is considered investigational.

Up to 30 participants will be enrolled in this study. All will take part at MD Anderson.

Study Parts and Study Drug Dose Levels:

If you are found to be eligible to take part in this study, you will start Part 1 of the study. During Part 1, you will receive the study drugs before having a stem cell transplant. If the disease is well controlled after the transplant and you are still eligible, you will start Part 2. During Part 2, you will continue to receive romidepsin. The study treatments given in each part are described in more detail below.

The dose of romidepsin you receive will depend on when you join this study. 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 romidepsin is found.

All participants will receive the same dose level of fludarabine. Busulfan dose levels are explained below.

Study Drug Administration and Transplant (Part 1):

The days before you receive the stem cell transplant are called minus days. The day you receive the stem cell transplant is called Day 0. The days after you receive the stem cell transplant are called plus days.

On Days -13 and -12, you will receive busulfan by vein over 3 hours. Blood (about 1 teaspoon each time) will then be drawn for pharmacokinetic (PK) testing up to 11 times over the 11 hours after the first busulfan dose. PK testing measures the amount of study drug in the body at different time points. The study staff will tell you more about the PK testing schedule. The test results will help the doctor decide what dose of busulfan you will receive during the study.

A heparin lock line will be placed in your vein before the PK testing to lower the number of needle sticks needed for these draws. If for any reason it is not possible for the PK tests to be performed, you will receive the standard dose of busulfan.

On Day -7, you will be admitted to the hospital.

On Day -6 through -3, you will receive romidepsin by vein over 4 hours, fludarabine by vein over 1 hour, and then busulfan by vein over 3 hours. PK testing up to 11 times over 11 hours will also be performed on Day -6 if the doctor thinks it is needed.

If you are going to be receiving a transplant from a matched unrelated donor, you will also receive antithymocyte globulin (ATG) by vein over 4 hours on the 3 days before the transplant. This drug is designed to further weaken your immune system to reduce the risk of rejecting of the transplant.

Beginning on Day -2, you will receive tacrolimus by vein over 24 hours every day until you are able to take it by mouth. Tacrolimus is designed to weaken the immune system and lower the risk of graft-versus-host-disease (GVHD - a reaction of the donor's immune cells against your body). Once you are able to take tacrolimus by mouth, you will take it every day for about 3 months, or until the doctor thinks it is safe to stop taking.

On Day 0, you will receive the donor's stem cells by vein. The infusion will last anywhere from about 30 minutes to several hours.

On Days +1, +3, +6, and +11, you will receive methotrexate by vein over about 15 minutes. Methotrexate is also designed to weaken the immune system and lower the risk of GVHD.

If the doctor thinks it is needed, you will be given other standard drugs to help lower the risk of side effects. You may ask the study staff for more information about how the drugs are given and their risks.

Romidepsin Maintenance Therapy (Part 2):

Starting between Day +28 and Day +100, if you are eligible for Part 2 based on the disease status, you will continue to receive romidepsin by vein over 1 hour once or twice a month. You may receive the doses at MD Anderson or at an oncologist's office close to where you live. The study doctor will discuss this with you.

Study Visits:

As a baseline test at the beginning of the study (within 7 days before starting romidepsin), blood (about 4 tablespoons) will be drawn for comparison purposes to learn if and how romidepsin may affect the disease and your immune system. If a bone marrow aspirate will be performed at this time, additional bone marrow aspirate will be collected for testing to see how romidepsin may have affected the disease and your immune system.

You will remain in the hospital for as long as the doctor thinks is needed.

Whenever your doctor thinks it is needed, blood (about 2 tablespoons) and/or urine will be collected for routine tests.

About ½-1, 3, 6, and 12 months after the transplant:

• You will have a physical exam.
• Blood (about 8 tablespoons) will be drawn to see how well the transplant has taken and to learn if and how romidepsin may have affected the disease and your immune system.
• If the doctor thinks it is needed, you will have a bone marrow aspiration to check the status of the disease. To collect a bone marrow aspirate, an area of the hip or other site is numbed with anesthetic, and a small amount of bone marrow is withdrawn through a large needle. Additional bone marrow aspirate will be collected for testing to see how romidepsin may have affected the disease and your immune system.

The above tests/procedures may be performed sooner, if your doctor thinks they are needed. You may also have additional tests if your doctor thinks they are needed.

Before your first dose of romidepsin in Parts 1 and 2:

• You will have an electrocardiogram (EKG) to check your heart function.
• Blood (about 4 tablespoons) will be drawn to learn if and how romidepsin may have affected the disease and your immune system. Part of this blood sample will be used for a pregnancy test if you can become pregnant.

If you are in Part 2, every 2 weeks (before each dose of romidepsin), blood (about 4 tablespoons) will be drawn for routine tests. Part of this blood sample will be used for a pregnancy test if you can become pregnant. This may be repeated more often, if your doctor thinks it is needed.

If you are in Part 2, once a month:

• You will have an EKG.
• You will have a physical exam.

Part 2 participants may have the blood tests done before each romidepsin dose and monthly EKGs and physical exams performed either at MD Anderson or your local oncologist's office. If they are performed locally, the results should be sent to the study staff. You will need to return to MD Anderson to have tests and procedures performed at 3, 6, and 12 months after the transplant.

Length of Study:

You may receive up to 4 doses of romidepsin in Part 1. You may also receive chemotherapy on certain days between Day -13 and Day -3, and the stem cell transplant on Day 0. In Part 2, you may receive up to 24 cycles of romidepsin maintenance therapy as part of the study.

Your participation on the study will be over after the follow-up visits. After 1 year, you will have routine follow-up with your transplant doctor.

You may be taken off study early if the doctor thinks it is in your best interest, if the disease gets worse or comes back, if intolerable side effects occur, if you have graft failure (the transplanted cells do not grow), or if you are unable to follow study directions.

If for any reason you want to leave the study early, you must talk to the study doctor. It may be life-threatening to leave the study after you have started to receive the study drugs but before you receive the stem cell transplant because your blood cell counts will be dangerously low.

Inclusion Criteria:

• Age 18 to 70 years of age.
• Diagnosis of either Cutaneous T-Cell Lymphoma; T-Prolymphocytic Leukemia; T-Large Granulocytic Leukemia; T-Lymphoblastic Leukemia/lymphoma; or Peripheral T-Cell Lymphoma, Natural Killer/T-cell lymphoma for whom allogeneic stem cell transplantation is indicated.
• An 10/10 or 8/8 HLA matched (high resolution typing at A, B, C, DRB1, DQ1) sibling or unrelated donor.
• EF>/= 50% on MUGA scan or Echocardiogram.
• FEV1, FVC and corrected DLCO >/= 40%.
• Adequate renal function, as defined by estimated serum creatinine clearance >/=50 ml/min (using the Cockcroft-Gault formula: creatinine clearance = [(140-age)*kg/(72*serum creatinine)] * 0.85 if female) and/or serum creatinine </=1.6 mg/dL. Renal function will be calculated using ideal body weight (IBW), unless a patient weights >40% of their IBW, then adjusted body weight will be utilized.
• Serum bilirubin </= 1.5 x upper limit of normal.
• SGOT and SGPT </= 2 x upper limit of normal.
• Able to sign informed consent.
• Men and women of reproductive potential must agree to follow accepted birth control methods for the duration of the study. Female subject is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study. Male subject agrees to use an acceptable method for contraception for the duration of the study.

Exclusion Criteria:

• Patient with active CNS disease.
• Pregnancy (positive Beta HCG test in a woman with child bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization) or currently breast-feeding. Pregnancy testing is not required for post-menopausal or surgically sterilized women.
• Active hepatitis B, either active carrier (HBsAg +) or viremic (HBV DNA >/=10,000 copies/mL, or >/= 2,000 IU/mL).
• Evidence of either cirrhosis or stage 3-4 liver fibrosis in patients with chronic hepatitis C or positive hepatitis C serology.
• HIV infection.
• Hematopoetic Transplant Co-Morbidity Index (HCT-CI) >4 unless deemed clinically insignificant by primary investigator for patients receiving Time-Sequential Busulfan (total exposure 20000 umol-min).
• Active uncontrolled bacterial, viral or fungal infections.
• Exposure to other investigational drugs within 4 weeks before enrollment.
• Grade >/= 3 non-hematologic toxicity from previous therapy that has not resolved to </= grade 1.
• Radiation therapy to head and neck (excluding eyes), and internal organs of chest, abdomen or pelvis in the month prior to enrollment.
• Prior whole brain irradiation.
• Prior autologous SCT in the prior 12 months.
• Congenital QT syndrome, QTc >500 ms.
• Myocardial infarction within 1 year of study entry. Subjects with a history of myocardial infarction between 6 and 12 months prior to study entry who are asymptomatic and have had a negative cardiac risk assessment (treadmill stress test, nuclear medicine stress test, or stress echocardiogram) since the event may participate;
• Other significant EKG abnormalities including 2nd degree atrio-ventricular (AV) block type II, 3rd degree AV block, or bradycardia (ventricular rate less than 50 beats/min);
• Symptomatic coronary artery disease (CAD), e.g., angina Canadian Class II-IV. In any patient in whom there is doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present;
• An EKG recorded at screening showing evidence of cardiac ischemia (ST depression depression of >/= 2 mm, measured from isoelectric line to the ST segment). If in any doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present;
• Congestive heart failure (CHF) that meets New York Heart Association (NYHA) Class II to IV definitions and/or ejection fraction <40% by MUGA scan or <50% by echocardiogram and/or MRI;
• A known history of sustained ventricular tachycardia (VT), ventricular fibrillation (VF), Torsade de Pointes, or cardiac arrest unless currently addressed with an automatic implantable cardioverter defibrillator (AICD);
• Hypertrophic cardiomegaly or restrictive cardiomyopathy from prior treatment or other causes;
• Uncontrolled hypertension, i.e., blood pressure (BP) of >/= 160/95; patients who have a history of hypertension controlled by medication must be on a stable dose and meet all other inclusion criteria; or,
• Any cardiac arrhythmia requiring an anti-arrhythmic medication (excluding stable doses of beta-blockers).
• Patients taking drugs leading to significant QT prolongation where the interaction is too great to proceed with romidepsin.
• Concomitant use of CYP3A4 inhibitors where the interaction is thought too great to proceed with romidepsin.