A Phase Ib Study of Belinostat With RDHAP Chemotherapy (Dexamethasone, Cytarabine, Cisplatinum) in Adults With Relapsed or Refractory Diffuse Large B-cell Lymphoma

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.