Inclusion Criteria:

• Patients must have histologically confirmed lymphoma in relapse or refractory to at least one prior systemic therapy. However, patients should be in relapse or refractory to appropriate standard salvage therapy, or have declined or are not deemed eligible for treatment with such salvage therapy including stem cell transplant. Diseases such as T-cell lymphomas, for which there is no standard salvage therapy, may enroll after failing only one prior systemic therapy.
• Patient must have measurable disease within lymph nodes, skin, or leukemic involvement of lymphoma
• Patient must have performance status of ≤2 on the ECOG Performance Scale. (See Section 6.1)
• Prior treatment with an anthracycline is permitted as long as the total doxorubicin dose (or equivalent) does not exceed 450mg/m2.
• Patients must have normal cardiac function, as evidenced by a left ventricular ejection fraction (LVEF) > 50%. A MUGA scan (echocardiogram may be used if MUGA scan is not available, but the same test must be used throughout the study) to evaluate LVEF must be done within 2 weeks prior to first dose of study drug.
• Patients with a minimum of 3 weeks since their last systemic treatment. Patients who have had prior treatment with an HDAC inhibitor may enroll after a 30-day washout period.
• Patients ≥ 18 years of age of any race, sex, and ethnicity
• Life expectancy of greater than 12 weeks.
• Female patient of childbearing potential has a negative serum pregnancy test β-hCG within 96 hours prior to receiving the first dose of vorinostat.
• Female patients with reproductive potential must use an adequate contraceptive method (e.g., abstinence, intrauterine device, oral contraceptives, barrier device with spermicide or surgical sterilization) during treatment and for three months after completing treatment.
• Male patient agrees to use an adequate method of contraception for the duration of the study.
• Patient must have adequate organ function as indicated by the following laboratory values:

System Laboratory Value Hematological Absolute neutrophil count (ANC) ≥1000 /mcL Platelets ≥75,000 /mcL Hemoglobin ≥ 9 g/dL Coagulation Prothrombin Time or INR ≤1.5x upper limit of normal (ULN) unless receiving therapeutic anticoagulation Partial thromboplastin time (PTT) ≤1.5x the ULN unless the patient is receiving therapeutic anticoagulation.

Chemistry K levels Normal limits Mg levels Normal limits Renal Serum creatinine or calculated creatinine clearance ≤2.0mg/dL OR ≥40 mL/min for patients with creatinine levels > 2.0mg/dL Hepatic Serum total bilirubin Normal limits AST (SGOT) and ALT (SGPT) ≤ 3 X ULN Alkaline Phosphatase (liver fraction) ≤ 3 X ULN a Creatinine clearance should be calculated per institutional standard.

• Patient, or the patient's legal representative, has voluntarily agreed to participate by giving written informed consent.
• Patient is ≥18 years of age on day of signing informed consent.
• Patient is available for periodic blood sampling, study related assessments, and management at the treating institution for the duration of the study.
• Eligibility of patients receiving any medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of vorinostat will be determined following review of their case by the Principal Investigator.

Exclusion Criteria:

• Patients with previously untreated lymphoma
• Patient who has had chemotherapy, radiotherapy, or biological therapy within 3 weeks prior to initial dosing with study drugs or who has not recovered from adverse events due to agents administered more than 3 weeks earlier.
• Patient is currently participating or has participated in a study with an investigational compound or device within 30 days of initial dosing with study drugs.
• Myocardial infarct within 6 months before enrollment, New York Heart Association (NYHA) Class II or greater heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, clinically significant pericardial disease, or electrocardiographic evidence of acute ischemic or active conduction system abnormalities
• QTc prolongation greater than 500ms
• Patient with a "currently active" second malignancy, other than non-melanoma skin cancer and carcinoma in situ of the cervix, should not be enrolled. Patients are not considered to have a "currently active" malignancy if they have completed therapy for a prior malignancy, are disease free from prior malignancies for >5 years or are considered by their physician to be at less than 30% risk of relapse.
• Patient is on any systemic steroids that have not been stabilized during the 3 weeks prior to the start of the study drugs.
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to vorinostat or doxorubicin.
• History of hypersensitivity reactions attributed to a conventional formulation of doxorubicin HCL or the components of PLD.
• Patients with active CNS metastases and/or carcinomatous meningitis are excluded. However, patients with CNS metastases who have completed a course of therapy would be eligible for the study provided they are clinically stable for 1 month prior to entry as defined as: (1) no evidence of new or enlarging CNS metastasis (2) off steroids or on a stable dose of steroids.
• Patient has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
• Patient is, at the time of signing informed consent, a regular user (including "recreational use") of any illicit drugs, substance abuse or had a recent history (within the last year) of drug or alcohol abuse.
• Patient is pregnant or breast feeding, or expecting to conceive or father children within the projected duration of the study. Pregnant women are excluded from this study because vorinostat and doxorubicin have the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with vorinostat or PLD, breastfeeding should be discontinued if the mother is treated with vorinostat and PLD.
• Patient has uncontrolled intercurrent illness or circumstances that could limit compliance with the study, including, but not limited to the following: active infection, acute or chronic graft versus host disease, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric conditions.
• Patient has a history or current evidence of any condition, therapy, or lab abnormality that might confound the results of the study, interfere with the patient's participation for the full duration of the study or is not in the best interest of the patient to participate.
• Patient has a history of a gastrointestinal surgery or other procedures that might, in the opinion of the investigator, interfere with the absorption or swallowing of the study drugs.
• HIV-positive patients receiving combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with vorinostat.
• Patients with known history of Hepatitis B or C are excluded.