Inclusion Criteria:

1. Histologically confirmed aggressive B-cell non-Hodgkin's lymphoma, specifically diffuse large cell and mantle cell lymphoma as identified in the World Health Organization (WHO) classification for non-Hodgkin's lymphomas.
2. Relapsed or refractory disease: Relapsed - Any number of prior therapies (including peripheral blood stem cell or bone marrow transplant) will be permitted. Refractory - Patients can have no more than two prior regimens excluding monotherapy with monoclonal antibody or radiation therapy.
3. Measurable disease, defined as at least one lesion whose longest diameter can be accurately measured as >/= 1.5 cm.
4. 18 years of age or older.
5. Laboratory values obtained </= 14 days prior to registration: Absolute neutrophil count (ANC) >/= 1,000/mm^3 or in patient with extensive bone marrow involvement (>50%) or hypersplenism with palpable splenomegaly, ANC >/= 500 mm^3; Platelets >/= 75,000/mm^3 or in patient with extensive bone marrow involvement (>50%) or hypersplenism with palpable splenomegaly, platelets >/= 50,000 mm^3; Total bilirubin </= upper limit of normal (ULN); Alkaline phosphatase </= 2 x ULN; AST </= 2 x ULN; Serum Creatinine </= ULN.
6. ECOG Performance Status (PS) 0, 1, or 2.
7. Cardiac function >/= 50% on MUGA (RVG).
8. Full recovery from all acute toxicities associated with prior therapy.
9. Capable of understanding the investigational nature, potential risks, and benefits of the study and able to provide valid informed consent. (For patients taking hydrochlorothiazide, furosemide, or other diuretics associated with potassium wasting: Must be on concurrent KCl supplementation or be switched to a potassium-conserving combination or a potassium-conserving diuretic).

Exclusion Criteria:

1. Transformed lymphoma, defined as the transformation of a low-grade lymphoma including follicular lymphoma or small lymphocytic lymphoma to a high-grade lymphoma, i.e. diffuse large cell lymphoma.
2. Diffuse large cell non-Hodgkin's lymphoma patients who are eligible for and willing to undergo stem cell transplant. As transplant represents a curative option for these patients, only patients who are ineligible for this procedure, or who have refused a stem cell transplant, or who have relapsed following a transplant may be considered for this study.
3. Any of the following as this regimen may be harmful to a developing fetus or nursing child: Pregnant women, Breastfeeding women, Men or women of childbearing potential or their sexual partners who are unwilling to employ adequate contraception (condoms, diaphragm, birth control pills, injections, intrauterine device [IUD], surgical sterilization, subcutaneous implants, or abstinence, etc.).
4. Significant cardiac disease including New York Heart association classification: · (a) Patients with know cardiac abnormalities such as Congenital long QT syndrome or QTc > 480 milliseconds (b) Patients who have had a myocardial infarction within 12 months of study entry (c) Patients who have a history of coronary artery disease (e.g. angina Canadian Class II - IV or positive stress imaging study) (d) Patients with an ECG recorded at screening showing evidence of cardiac ischemia (ST depression of > 2 mm) (continued #5)
5. (e) Patients with congestive heart failure that meets NYHA Class II to IV definitions and /or ejection fraction < 50% by MUGA scan or echocardiogram. (f) Patients with a history of sustained VT, VF, Torsades de Pointes, or cardiac arrest unless currently addressed with an automatic implantable cardioverter defibrillator (g) Patients with hypertrophic or restrictive cardiomyopathy from prior treatment or other causes and patients with significant left ventricular hypertrophy. (h) Patients with uncontrolled hypertension (i.e. > 160/95) (continue #6)
6. (i) Patients with any cardiac arrhythmia requiring anti-arrhythmic medication other than a beta blocker or calcium channel blocker. Patients in whom digitalis cannot be discontinued are excluded from study. (j) Patients with Mobitz II second degree block who do not have a pacemaker. Patients with first degree or Mobitz I second degree block, bradyarrhythmias or sick sinus syndrome require Holter monitoring and evaluation by cardiology.(k) Patients with other cardiac disease may be excluded at the discretion of the PI following consultation with cardiology.
7. Medication with any drug associated with QTc prolongation.
8. Prior doxorubicin >/= 450 mg/m^2 or mitoxantrone >/= 112 mg/m^2. Patients who have received both mitoxantrone and doxorubicin should have a "doxorubicin equivalent dose" < 450 mg/m^2 (doxorubicin equivalent dose = mitoxantrone dose (mg/m^2) x 4 + doxorubicin dose (mg/m^2).
9. Known HIV disease. Note: These individuals are excluded from this early phase trial because of potential pharmacokinetic interactions between the investigational agent and their anti-retroviral medications that might compromise their HIV therapy as well as alter the pharmacokinetics of the investigational compound. In addition, these patients are at greater risk of myelosuppression due to their HIV disease and therapy.
10. CNS lymphoma.
11. Other uncontrolled serious medical condition or active infection (e.g. chronic obstructive pulmonary disease, diabetes, etc.). Prior therapy with a histone deacetylase inhibitor.