A Study to Evaluate the Safety and Efficacy of Dasatinib (Sprycel) in Subjects With Relapsed or Refractory Diffuse Large B-Cell Lymphoma (DLBCL)

Inclusion Criteria: * Must understand and voluntarily sign an informed consent form. * Must be \> = 18 years of age at the time of signing the informed consent form. * Must be able to adhere to the study visit schedule and other protocol requirements. * Biopsy-proven aggressive Diffuse Large B-Cell Lymphoma. * Relapsed or refractory to previous therapy for lymphoma. * Subjects must have received at least one prior combination chemotherapy regimen. There is no limit on the number of prior therapies. * Subjects who have relapsed following an autologous stem cell transplant are eligible. * Subjects must have measurable disease on cross sectional imaging that is at least 2 cm in the longest diameter. * Eastern Cooperative Oncology Group (ECOG) performance status score of 0, 1, or 2. * Life expectancy of \> = 90 days (3 months). * Ability to take oral medication: dasatinib tablets may be swallowed as a whole. * Adequate organ function: Total bilirubin \<2.0 times Upper Limit of Normal (ULN) Serum Na, K, Mg, Phos, and Ca \> Lower Limit of Normal (LLN) Hemoglobin, neutrophil count, platelets, PT/PTT all grade 0-1 Serum creatinine concentration \<1.5 x institutional upper limit of normal (ULN). Serum SGOT/AST or SGPT/ALT \< 2.5 x institutional upper limit of normal (ULN). * Concomitant medications: 1. Patient agrees to discontinue St. Johns Wort while receiving dasatinib 2. IV biphosphonates will be withheld for the first 8 weeks of dasatinib therapy due to risk of hypocalcemia. * Females of childbearing potential (FCBP) must agree to use two reliable forms of contraception simultaneously or to practice complete abstinence from heterosexual intercourse during the following time periods related to this study: 1) for at least 28 days before starting study drug; 2) while participating in the study; and 3) for at least 28 days after discontinuation from the study. The two methods of reliable contraception must include one highly effective method (i.e. intrauterine device (IUD), hormonal \[birth control pills, injections, or implants\], tubal ligation, partner's vasectomy) and one additional effective (barrier) method (i.e. latex condom, diaphragm, cervical cap). FCBP must be referred to a qualified provider of contraceptive methods if needed. * Before starting study drug: * Female Subjects: FCBP must have two negative pregnancy tests (sensitivity of at least 50 mIU/mL) prior to starting study drug. The first pregnancy test must be performed within 10-14 days prior to the start of study drug and the second pregnancy test must be performed within 24 hours prior to the start of study drug. The subject may not receive study drug until the Investigator has verified that the results of these pregnancy tests are negative; Will be warned that sharing study drug is prohibited and will be counseled about pregnancy precautions and potential risks of fetal exposure; Must agree to abstain from donating blood during study participation and for at least 28 days after discontinuation from the study. * Male Subjects: Must agree to use a latex condom during sexual contact with females of childbearing potential while participating in the study and for at least 28 days following discontinuation from the study even if he has undergone a successful vasectomy; Will be warned that sharing study drug is prohibited and will be counseled about pregnancy precautions and potential risks of fetal exposure; Must agree to abstain from donating blood, semen, or sperm during study participation and for at least 28 days after discontinuation from the study. * During study participation and for 28 days following discontinuation from the study: * All Subjects: No more than a 30-day supply of study drug will be dispensed at a time. Female Subjects: * FCBP with regular cycles must agree to have pregnancy tests weekly for the first 28 days of study participation and then every 28 days while on study, at study discontinuation, and at day 28 following discontinuation from the study. If menstrual cycles are irregular, the pregnancy testing must occur weekly for the first 28 days and then every 14 days while on study, at study discontinuation, and at days 14 and 28 following discontinuation from the study. * In addition to the required pregnancy testing, the Investigator must confirm with FCBP that she is continuing to use two reliable methods of birth control at each visit. * Counseling about pregnancy precautions and the potential risks of fetal exposure must be conducted at a minimum of every 28 days. During counseling, subjects must be reminded to not share study drug and to not donate blood. * Pregnancy testing and counseling must be performed if a subject misses her period or if her pregnancy test or her menstrual bleeding is abnormal. Study drug treatment must be discontinued during this evaluation. * Females must agree to abstain from breastfeeding during study participation and for at least 28 days after discontinuation from the study. Male Subjects: * Counseling about the requirement for latex condom use during sexual contact with females of childbearing potential and the potential risks of fetal exposure must be conducted at a minimum of every 28 days. During counseling, subjects must be reminded to not share study drug and to not donate blood, sperm, or semen. * If pregnancy or a positive pregnancy test does occur in a study subject or the partner of a male study subject during study participation, study drug must be immediately discontinued. Exclusion Criteria: * Subjects who are candidates for and willing to undergo an autologous stem cell transplant. * Subjects who are post allogeneic stem cell transplant. * All subjects with active central nervous system (CNS) lymphoma. Subjects with previous CNS lymphoma that have been treated with chemotherapy, radiotherapy or surgery who have remained asymptomatic for 90 days (3 months) and demonstrate, no CNS lymphoma, as shown by lumbar puncture, CT scan or MRI, are eligible. (If required, lumbar puncture, CT or MRI should be performed during screening process.) Subjects should not be receiving corticosteroids. * Prior history of malignancies other than NHL (except for basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the cervix or breast) unless the subject has been free of the disease for \> = 365 days (1 year). * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject from signing the informed consent form. * Known positive for HIV. * Pregnant or lactating females. * Concomitant Medications: Category I drugs that are generally accepted to have a risk of causing Torsades de Pointes including: (Patients must discontinue drug 7 days prior to starting dasatinib) quinidine, procainamide, disopyramide, amiodarone, sotalol, ibutilide, dofetilide, erythromycin, clarithromycin, chlorpromazine, haloperidol, mesoridazine, thioridazine, pimozide, cisapride, bepridil, droperidol, methadone, arsenic, chloroquine, domperidone,halofantrine, levomethadyl, pentamidine, sparfloxacin, lidoflazine * Concurrent medical condition which may increase the risk of toxicity, including: 1. Pericardial or pleural effusion of any grade 2. Clinically-significant coagulation or platelet function disorder (e.g. known von Willebrand's disease) * History of significant bleeding disorder unrelated to cancer, including: 1. Diagnosed congenital bleeding disorders (e.g., von Willebrand's disease) 2. Diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies) 3. Ongoing or recent (\< = 3 months) clinically significant gastrointestinal bleeding * Cardiac symptoms within 6 months: 1. Uncontrolled angina, congestive heart failure, or MI 2. History of clinically significant ventricular arrythmias: fibrillation, Torsades de pointes, or tachycardia. 3. Prolonged QTc interval on pre-entry electrocardiogram (\> 450msec). * Prior use of dasatinib. * Use of any standard or experimental anti-cancer drug therapy within 28 days of the initiation (Day 1) of study drug therapy. * Known active Hepatitis B or C. * Prisoners or subjects who are compulsorily detained (involuntarily incarcerated) for treatment of either a psychiatric or physical (e.g., infectious) illness.