Relapsed and/or Refractory Non-Hodgkin Lymphoma Study

Inclusion Criteria: * Histologically confirmed non-Hodgkin Lymphoma including small lymphocytic lymphoma, lymphoplasmacytic lymphoma, follicular center cell lymphoma, mantle cell lymphoma, marginal zone lymphoma, diffuse large B cell lymphoma, Burkitt's lymphoma, lymphoblastic lymphoma, anaplastic large cell lymphoma, nasal NK/T cell lymphoma, mycosis fungoides/Sezary syndrome, angioimmunoblastic T-cell lymphoma and peripheral T-cell lymphomas not otherwise specified * Received 2 or \> prior therapies, which may include hematopoietic cell transplant (HCT) * Received treatment with a nucleoside analog, or an alkylating agent, an anthracycline and/or in the case of B cell lymphomas, rituximab * Resistant disease to 2 regimens or resistant disease to at least 1 regimen after first relapse * Bi-dimensionally measurable disease documented within 30 days prior to enrollment. Bidimensionally measurable disease is defined as: * A lymph node or tumor mass that can be accurately measured in two dimensions by CT,MRI, medical photograph (skin or oral lesion), plain X-ray, PET scan or other conventional technique and a greatest diameter of 1 cm or \>; or palpable lesions with both diameters \> 2 cm (lesion measured in 2 largest perpendicular dimensions in millimeters) * For the purposes of this protocol, disease should be located in an area of no prior radiation therapy or a clear progression in an area that was previously irradiated * Adequate organ and marrow function obtained \< or = to 14 days prior to enrollment as defined by a(n): * ANC \> or = to 1,000/microliter * Platelet count \> or = to 100,000/microliter, or \> or = to 75,000/microliter if the bone marrow is involved * Hemoglobin level \> or = to 9 g/dL * Total bilirubin \< or = to 1.5 x institutional upper limit of normality (ULN).(If abnormal, direct bilirubin less than or equal to 1.5 x institutional ULN) * ALT or AST \< or = to 2.5 x institutional ULN (\< or = to 5 x institutional ULN if liver involvement with lymphoma) * Serum creatinine \< or = to 1.5 x institutional ULN * Zubrod (ECOG) Performance Status of 0 or 1 * Age \> than or = to 18 years * Life expectancy \> or = to 3 months as clinically determined by referring physician * Female patient is either post menopausal, free from menses for \> 2 years, surgically sterilized or willing to use highly effective methods of contraception (i.e., a condom in conjunction with a diaphragm, or spermicidal jelly; or oral, injectable, or implanted birth control; or abstinence ) to prevent pregnancy throughout the study, starting with visit 1 * Female patients of childbearing potential must have a negative serum pregnancy test (beta-HCG) within 72 hours of enrollment and should not be nursing due to the potential for congenital abnormalities and of harm to nursing infants due to this treatment regimen * Male patient agrees to use an adequate method of contraception (i.e., a condom if female partner uses a diaphragm, spermicidal jelly; or oral, injectable, or implanted birth control; or abstinence) for the duration of the study and for 12 weeks after the last dose * Patient must be able to swallow capsules * Signed and dated IRB/ethics committee-approved informed consent before any protocol specific screening procedures are performed * Both men and women of all races and ethnic groups are eligible for this trial Exclusion Criteria: * Prior investigational therapy within 3 weeks of enrollment. Investigational therapy is defined as treatment that is not approved for any indication * CNS metastases, as indicated by clinical symptoms,cerebral edema, requirement for corticosteroids and/or progressive growth (treated CNS metastases must be stable for greater than 2 weeks prior to enrollment) * Active second malignancy that requires treatment or that would interfere with assessment of response * Prior malignancy, except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer with \< 5 years of documented disease-free status * Treatment with the following within the timeframe specified prior to enrollment: * Chemotherapy, radiotherapy, immunotherapy (active (such as vaccines) or passive (such as monoclonal antibodies or immunotoxins)) or major surgery \< or = to 3 weeks; * Nitrosourea, or mitomycin \< or = to 6 weeks * Radioimmunotherapy (e.g. Bexxar or Zevalin) \< or = to 12 weeks * Concurrent enzyme-inducing anticonvulsant agents or valproic acid in last 4 weeks * Prior bortezomib or any other proteasome inhibitor * Prior vorinostat or any other histone deacetylase inhibitor * Concurrent systemic corticosteroids (\<10 mg/day of prednisone or equivalent for adrenal insufficiency or acute allergic reactions allowed) * Uncontrolled current illness including, but not limited to: * Clinically or laboratory determined active infection * Clinically limiting congestive heart failure or ejection fraction (EF) \<45% * Clinically unstable angina pectoris (or myocardial infarction within 6 months of Day 1) * Clinically significant cardiac arrhythmia * Limiting pulmonary hypertension * Pre-existing neuropathy ≥ grade 2 * Patients with pleural effusions, ascites or peripheral edema grade 2 or \> * HIV * Active viral hepatitis * Major surgery or significant traumatic injury within 21 days prior to enrollment (this does not apply to placement of a venous access device) * Hypersensitivity to any of the components in vorinostat or bortezomib or agents containing boron or mannitol * Significant psychiatric illness/social situations that would limit compliance with study medication and requirements of the study as determined by study MD * Significant medical illness or abnormal laboratory finding that would, in the investigator's judgment, increase the subject's risk by participating in this study