MLN4924 Compared With MLN4924 Plus Chemotherapy for Large B-cell Lymphoma

* INCLUSION CRITERIA: * Biopsy-proven relapsed or refractory Large B-cell lymphoma. * Confirmed pathological diagnosis by the Laboratory of Pathology, NCI. * Age greater than or equal to 18 years. * ECOG performance status 0-2. * Adequate renal function or creatinine clearance \> 50 ml/min/1.73m(2) unless lymphoma related. * Adequate hepatic and hematological function, as defined by: * Bilirubin must be less than or equal to ULN, except less than or equal to 2 mg/dl (total) in patients with Gilbert s syndrome (as defined by \> 80% unconjugated hyperbilirubinemia); * ALT and AST must be less than or equal to Grade 1. * ANC \> 1000 and platelets \> 75,000 unless lymphoma related. * Prothrombin time (PT) and activated partial thromboplastin time (aPTT) must be less than or equal to 1.5 times the upper limit of the normal range (ULN); except if, in the opinion of the Investigator, the aPTT is elevated because of a positive Lupus Anticoagulant. * Left ventricular ejection fraction (LVEF) \> 45% as assessed by echocardiogram or MUGA * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care. * Female subject is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study. * Male patients must use an appropriate method of barrier contraception (eg, condoms), inform any sexual partners that they must also use a reliable method of contraception (ie, a hormonal contraceptive, an intrauterine device, diaphragm with spermicide, or abstinence), and refrain from blood and semen donation during the study and for 4 months after the last dose of study treatment. EXCLUSION CRITERIA: * Female subject pregnant or breast-feeding. Confirmation that the subject is not pregnant must be established by a negative serum Beta-human chorionic gonadotropin (Beta-hCG) pregnancy test result obtained during screening. Pregnancy testing is not required for women without child-bearing potential. * History of a prior invasive malignancy in past 5 year. * Myocardial infarction 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 has to be documented by the investigator as not medically relevant. * Patient has greater than or equal to Grade 2 peripheral neuropathy within 14 days before enrollment * Serious concomitant medical illnesses that would jeopardize the patient s ability to receive the regimen with reasonable safety. * HIV positive patients * Systemic cytotoxic therapy within 3 weeks of treatment * Serious medical or psychiatric illness likely to interfere with participation in this clinical study. * CYP3A inducers within 14 days before the first dose of MLN4924. Moderate and strong CYP3A inhibitors and CYP3A inducers are not permitted during the study. Patients must have no prior history of chronic amiodarone use in the 6 months prior to the first dose of MLN4924. * Patients currently taking statins who are unwilling or unable to refrain from using statins on the day prior to, day of, and day after each MLN4924 administration * Diarrhea \> Grade 1, based on the NCI CTCAE categorization despite use of optimal antidiarrheals * Known hepatitis B surface antigen-positive, or known or suspected active hepatitis C infection * Clinically uncontrolled central nervous system (CNS) involvement (Patients who have a history of CNS involvement, but no evidence of active CNS disease are not excluded.) * Ongoing anticoagulant therapy (eg, aspirin, Coumadin, heparin) that cannot be held to permit bone marrow sampling. Patients who require anticoagulant therapy, and can not be maintained on low molecular weight heparin should not be considered for this study. INCLUSION OF WOMEN AND MINORITIES: -Both men and women and members of all races and ethnic groups are eligible for this trial.