Inclusion Criteria:

• Inclusion Criteria for Autologous Transplant:
• Diagnosis of NHL, transformed B-cell lymphoma, follicular lymphoma, mantle cell lymphoma, diffuse large B-cell or T-cell lymphoma, and deemed a candidate for autologous transplant
• American Heart Association Class I: patients with cardiac disease but without resulting limitation of physical activity; ordinary physical activity does not cause undue fatigue, palpitation, dyspnea, or anginal pain; additionally, patients > 60 years of age must have a left ventricular ejection fraction of at least >= 40% demonstrated by multi gated acquisition scan (MUGA) or echocardiogram (ECG)
• Total bilirubin (TB) =< 1.5 mg/dL
• Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =< 3x the upper limit of normal (ULN)
• Creatinine clearance (CrCL) (calculated creatinine clearance is permitted) > 40 mL/min
• Diffusing capacity of carbon monoxide (DLCO), forced expiratory volume in one second (FEV1), and forced vital capacity (FVC) >= 50% of predicted (corrected for hemoglobin)
• Autologous graft with a minimum of >= 3.0 x 10^6 CD34+ cells/kg; not CD34 selected
• Signed informed consent
• Female patients of childbearing potential has a negative serum pregnancy test beta-human chorionic gonadotropin (hCG)
• Female patient is either post menopausal, free from menses for >= 2 years, surgically sterilized, or willing to use 2 adequate barrier methods of contraception to prevent pregnancy or agrees to abstain from heterosexual activity throughout the study
• Male patient agrees to use an adequate method of contraception for the duration of the study
• Inclusion Criteria for Maintenance Therapy:
• 30-120 days post ASCT for non-Hodgkin's lymphoma: CrCL >= 40 ml/min; platelets (PLT) >= 75,000, and absolute neutrophil count (ANC) >= 1500 cells/mm^3 for 5 days after recovery from ASCT nadir; TB =< 1.5 x ULN, AST/ALT =< 2.5 x ULN

Exclusion Criteria:

• Exclusion Criteria for Transplant:
• Karnofsky performance score < 70%
• Uncontrolled bacterial, viral, or fungal infection (currently taking medication and with progression or no clinical improvement)
• Pregnant or breastfeeding
• Fertile men and women unwilling to use contraceptive techniques from the time of transplant until one month post maintenance therapy
• Prior autologous or allogeneic hematopoietic stem cell transplantation (HSCT)
• Patients with evidence of myelodysplastic syndromes (MDS)/acute myeloid leukemia (AML) or abnormal cytogenetics analysis indicative of MDS on the pre-transplant bone marrow examination
• Prolonged QTC on electrocardiogram (EKG)
• Poorly-controlled diabetes mellitus (DM)
• >= grade 2 peripheral neuropathy
• Prior history of human immunodeficiency virus (HIV) positivity or known history of hepatitis B or C
• Previous history of hypersensitivity to Bortezomib, boron, or mannitol; known hypersensitivity to the components of study drug or its analogs
• Require therapeutic anticoagulation treatment, especially with coumadin
• Patient who has had chemotherapy, radiotherapy, or biological therapy, within 30 days (42 days for nitrosoureas or mitomycin C) or who has not recovered from adverse events due to agents administered more than 30 days earlier
• Patient is currently participating or has participated in a study with an investigational compound or devise within 30 days of initial dosing with study drug(s)
• Patient had prior treatment with an histone deacetylase (HDAC) inhibitor (e.g., romidespin [Depsipeptide], NSC-630176, MS 275, LAQ-824, belinostat [PXD-101], LBH589, MGCD0103, CRA024781, etc); patients who have received compounds with HDAC inhibitor-like activity, such as valproic acid, as anti-tumor therapy should not enroll in this study; patients who have received such compounds for other indications, e.g. valproic acid for epilepsy, may enroll after a 30-day washout period
• History of central nervous system (CNS) disease
• Symptomatic ascites or pleural effusions
• 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 of any illicit drugs, substance abuse or had a recent history (within the last year) of drug or alcohol abuse
• Patient with a history of a prior malignancy with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma or an in situ malignancy; adequately treated localized prostate carcinoma with prostate-specific antigen (PSA) < 1.0; or who has undergone potentially curative therapy with no evidence of disease for five years, and/or who is deemed at low risk for recurrence by his/her treating physician
• 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
• Exclusion Criteria for Maintenance Therapy:
• >= grade 2 peripheral neuropathy within 14 days before beginning maintenance therapy
• Prolonged QTC
• Poorly controlled DM
• Myocardial infarction (MI) with ASCT or developed dilated cardiomyopathy with ASCT
• Untreated systemic infection
• Potassium (K) and magnesium (Mg) < normal limits of adequate supplementation
• Patient had MI within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities; prior to study entry, any ECG abnormality at screening must be documented by the investigator as not medically relevant
• Patient has hypersensitivity to VELCADE, boron, or mannitol
• Female subject is pregnant or lactating; confirmation that the subject is not pregnant must be established by a negative serum beta-hCG pregnancy test result obtained during screening; pregnancy testing is not required for postmenopausal or surgically sterilized women
• Female patients who are lactating or have a positive serum pregnancy test during the screening period, or a positive urine pregnancy test on Day 1 before first dose of study drug, if applicable
• Serious medical or psychiatric illness likely to interfere with participation in this clinical study
• Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy
• Participation in clinical trials with other investigational agents not included in this trial, within 14 days of the start of this trial and throughout the duration of this trial
• Radiation therapy within 3 weeks before randomization; enrollment of subjects who require concurrent radiotherapy (which must be localized in its field size) should be deferred until the radiotherapy is completed and 3 weeks have elapsed since the last date of therapy