Inclusion Criteria:

* Biopsy-proven (no needle aspirations or cytologies) aggressive B-cell non-Hodgkin's lymphoma (NHL), including 1 of the following histology subtypes:

* Diffuse large cell NHL
* Burkitt's or Burkitt-like NHL
* Primary mediastinal NHL
* Relapsed or refractory disease
* Bidimensionally measurable disease
* Transformed NHL allowed
* Not eligible for stem cell transplantation (for patients registered to study at first relapse)
* No active CNS involvement by lymphoma
* Zubrod performance status 0-2
* No history of allergic reactions attributed to compounds of similar chemical or biologic composition to PXD101
* Absolute neutrophil count >= 1,500/mm\^3
* Platelet count>=100,000/mm\^3
* WBC >= 3,000/mm\^3
* Creatinine < 2 times upper limit of normal (ULN) OR creatinine clearance >= 60 mL/min
* No significant EKG abnormalities
* Bilirubin normal
* SGOT/SGPT < 2.5 times ULN (=< 5 times ULN if liver involvement)
* No long QT syndrome or marked baseline prolongation of QT/QTc interval (e.g., repeated demonstration of QTc interval > 500 msec)
* No other significant cardiovascular disease, including any of the following:

* Unstable angina pectoris
* Uncontrolled hypertension
* Congestive heart failure related to primary cardiac disease
* Any condition requiring anti-arrhythmic therapy
* Ischemic or severe valvular heart disease
* Myocardial infarction within the past 6 months
* No major surgery within 28 days prior to study entry
* No concurrent combination antiretroviral therapy for HIV-positive patients
* No concurrent medication that may cause Torsades de Pointes (i.e., prolongation of the QT interval > 500 msec)
* At least 14 days since prior radiotherapy
* At least 2 weeks since prior valproic acid or any other histone deacetylase inhibitor
* No clinical evidence of any of the following:

* Severe peripheral vascular disease
* Diabetic ulcers or venous stasis ulcers
* History of deep venous or arterial thrombosis within the past 3 months
* Radioimmunotherapy is considered a chemotherapy regimen
* Single-agent rituximab is not considered a chemotherapy regimen
* Standard salvage chemotherapy followed by autologous stem cell transplantation is considered 1 regimen
* No known AIDS or HIV-associated complex
* Not pregnant or nursing
* Fertile patients must use effective contraception
* No other malignancy within the past 5 years except adequately treated basal cell or squamous cell skin cancer or in situ carcinoma of the cervix
* At least 2 weeks since prior therapy and recovered
* No more than 5 prior chemotherapy regimens