Withdrawal of study support.

The goal of this clinical research study is to find the highest tolerable dose of belinostat that can be combined with standard chemotherapy drugs (rituximab, cisplatin, cytarabine, and dexamethasone) in patients with relapsed or refractory DLBCL who are eligible for an autologous stem cell transplant (a transplant of the patient's own stem cells). The safety of the study drug will also be studied.

Study Groups:

If participant is found to be eligible to take part in this study, they will be assigned to a dose level of belinostat based on when they join this study. Up to 4 dose levels of belinostat will be tested. Between 3-6 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 belinostat is found.

All participants will receive the same dose level of the standard chemotherapy drugs.

Study Drug Administration:

Participant will receive belinostat with standard chemotherapy for up to two 21-day cycles.

Participant will receive belinostat by vein on Days 1 and 2 of each cycle. The infusions will last 24 hours.

Participant will receive rituximab and cisplatin by vein on Day 2 of each cycle. Participant will receive cytarabine by vein on Day 2 or 3 of each cycle, depending on when they join this study. Rituximab will be given over 4-5 hours, cisplatin will be given over 3-4 hours, and cytarabine will be given over 1 hour.

Participant will take dexamethasone once a day by mouth on Days 2-5 of both study cycles.

Blood (about 5 tablespoons) and bone marrow will be collected about 10 business days (Monday-Friday) before participant begins receiving belinostat. The blood and bone marrow will be used for peripheral blood mononuclear cell (PBMC) testing. This testing is designed to learn if participant will respond to treatment. To collect a bone marrow biopsy, an area of the hip or other site is numbed with anesthetic, and a small amount of bone marrow is withdrawn through a large needle.

Participant will also receive filgrastim, pegfilgrastim, SMX, valacyclovir, ciprofloxacin and fluconazole to reduce side effects. Participant's study doctor will discuss with them when and how they will take these drugs.

If participant's doctor thinks it is necessary, they will also have a bone marrow biopsy and aspirate performed to check the status of the disease within 4 weeks before they begin receiving belinostat. To collect a bone marrow biopsy/aspirate, an area of the hip or other site is numbed with anesthetic, and a small amount of bone marrow and bone is withdrawn through a large needle.

Study Visits:

Within 5 working/business days before the start of each cycle:

• Participant will have a physical exam.
• Blood (about 4-6 tablespoons) will be drawn for routine tests.

One (1) time a week after the completion of therapy during each cycle, blood (about 4-6 tablespoons) will be drawn for routine tests.

Blood (about 4 tablespoons) will be drawn on Days 1,2, 3, and 21 (+/- 72 hours) of Cycles 1 and 2 for PBMC testing.

Length of Treatment:

Participant may continue taking belinostat combined with chemotherapy for up to 3 cycles. Participant will no longer be able to take the study drugs if the disease gets worse, if intolerable side effects occur, or if they are unable to follow study directions.

Patient's participation on the study will be over after the follow-up visits.

End-of-Dosing Visit:

Within 3 weeks after the start of the last cycle:

• Participant will have a physical exam.
• Blood (about 4-6 tablespoons) will be drawn for routine and PBMC testing.
• Participant will have an FDG-PET/CT scan to check the status of the disease.
• If participant's doctor thinks it is necessary, they may have a bone marrow biopsy and aspirate to check the status of the disease
• If participant's doctor thinks it is necessary, they may have a core needle biopsy to check the status of the disease. To perform a core biopsy, a sample of tissue is removed using a hollow core needle that has a cutting edge.

This is an investigational study. Belinostat is FDA approved to treat T-cell lymphoma. Its use in this study is investigational. The standard chemotherapy drugs are commercially available and FDA approved to treat DLBCL.

Up to 40 participants will be enrolled on this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Aggressive B-cell lymphoma, including DLBCL and FL or other indolent or low grade malignancy transforming to DLBCL, Grade III FL, Burkitt lymphoma, and unclassifiable B-cell lymphoma with features of Burkitt and DLBCL according to the World Health Organization, with biopsy confirmation of disease which has relapsed after or refractory to a standard cytotoxic chemotherapy combination including rituximab and doxorubicin, for whom an autologous stem cell transplant is planned.
2. Have received between 1 - 2 prior cytotoxic treatments, not to include belinostat, RDHAP, or autologous or allogeneic stem cell transplant. Radiation which was pre-planned to occur at the conclusion of systemic cytotoxic therapy will not be considered a separate prior therapy. Radiation administered for potential recurrent or relapsed disease will be considered a separate prior therapy.
3. Patient or durable power of attorney (DPA) for healthcare must be able to understand and voluntarily sign an IRB-approved informed consent form.
4. Age 18-80 years at the time of signing the informed consent.
5. Patients must have bi-dimensional measurable disease.
6. Patients with performance status of </=3 (Eastern Cooperative Oncology Group Performance Status Scale, 3 only allowed if decline in status is deemed related to lymphoma and felt potentially reversible by the treating physician).
7. Within 4 weeks of therapy start, serum bilirubin <1.5x ULN (maximum level based on MD Anderson laboratory ranges is 1.95 mg/dL); AST (SGOT) and ALT (SGPT) </=3x ULN or < 5x ULN if hepatic metastases are present; ANC >1000/mm^3 and platelets >100,000/mm^3 unless deemed likely related to lymphoma involvement in the bone marrow where the minimum ANC allowable will be 500/mm^3 and minimum allowable platelet count will be 50,000/mm^3.
8. Within 4 weeks of therapy start, renal function assessed by calculated creatinine clearance >/= 50ml/min by Cockcroft-Gault formula using actual body weight.
9. Patients must be willing to receive transfusions of blood products.
10. Within 4 weeks of therapy start, women of childbearing potential must have a negative serum (Beta-human chorionic gonadotropin [Beta-hCG]) or urine pregnancy test at screening and must adhere to the scheduled pregnancy testing.
11. Women of childbearing potential and men who are sexually active with a woman of childbearing potential must be practicing a highly effective method of birth control during and after the study (12 months for women and 3 months for men), consistent with local regulations regarding the use of birth control methods for subjects participating in this clinical study.

Exclusion Criteria:

1. Any serious medical condition including but not limited to uncontrolled hypertension, uncontrolled diabetes mellitus, active/symptomatic coronary artery disease, COPD, left ventricular ejection fraction of less than 40, active infection, active hemorrhage, or psychiatric illness that, in the investigators opinion places the patient at unacceptable risk and would prevent the subject from signing the informed consent form. Patients with history of cardiac arrhythmias should have cardiac evaluation and clearance.
2. Pregnant or lactating females.
3. Known hypersensitivity to any component of RDHAP.
4. Patients with Gilbert's syndrome unless homozygosity for the UFT1A1*28 mutation has been excluded.
5. HIV infection, active hepatitis B infection, active hepatitis C infection.
6. Known homozygous for UGT1A1*28 mutation from prior testing or family history.
7. Requirement of therapy with a UGT1A1 Inhibitor, as detailed in Section 8.4, or use within 7 days of enrollment on this protocol.
8. All patients with active central nervous system involvement with lymphoma.
9. Diagnosis of prior malignancy within the past 2 years with the exception of successfully treated basal cell carcinoma, squamous cell carcinoma of the skin, carcinoma "in situ" of the cervix or breast. History of other malignancies are allowed if in remission (including prostate cancer patients in remission from radiation therapy, surgery or brachytherapy), not actively being treated, with a life expectancy > 3 years.
10. Significant neuropathy (Grades 3 - 4, or Grade 2 with pain) within 14 days prior to enrollment.