Inclusion Criteria:

- Patients must have a histologically or cytologically confirmed lymphoid malignancy
(like Hodgkin lymphoma or one of the mature B- or T-cell non-Hodgkin lymphomas as
classified by World Health Organization [WHO]) for which standard curative or
palliative measures do not exist or are no longer effective

- Patients must have measurable disease in two dimensions and >= 2 cm is acceptable (or
1.5 cm if 0.5 slices are used, as in spiral computed tomography [CT] scans); lesions
that are considered intrinsically non-measurable include the following:

- Bone lesions

- Leptomeningeal disease

- Ascites

- Pleural/pericardial effusion

- Inflammatory breast disease

- Lymphangitis cutis/pulmonis

- Abdominal masses that are not confirmed and followed by imaging techniques

- Cystic lesions

- Lesions that are situated in a previously irradiated area

- Patients must have had at least 1 prior systemic chemotherapy (not just steroids or
local radiation)

- Patients with known brain metastases should be excluded from this clinical trial

- Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%)

- Life expectancy of greater than 12 weeks

- Absolute neutrophil count ≥ 1,500/mcL

- Platelets ≥ 100,000/mcL

- Total bilirubin < 1.5 times institutional upper limit of normal (ULN); patients with
elevation of indirect (unconjugated) bilirubin alone, as in Gilbert's syndrome, are
eligible

- Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
[SGOT])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase [SGPT])
< 2.5 times institutional ULN

- Creatinine ≤ institutional upper limit of normal OR creatinine clearance ≥ 60
mL/min/1.73 m^2 for patients with creatinine levels above institutional normal

- Women of child-bearing potential and men must agree to use adequate contraception
(hormonal or barrier method of birth control; abstinence) prior to study entry, for
the duration of study participation, and 4 months after completion of MLN8237
administration

- No history of allergic reactions attributed to compounds of similar chemical or
biologic composition to MLN8237 including, but not limited to, established allergic
reaction to benzodiazepines

- No uncontrolled intercurrent illness including, but not limited to, ongoing or active
infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
arrhythmia, or psychiatric illness/social situations that would limit compliance with
study requirements

- Pregnant women are excluded from this study; breastfeeding should be discontinued if
the mother is treated with MLN8237

- No known history of uncontrolled sleep apnea syndrome or other conditions that could
result in excessive daytime sleepiness, such as severe chronic obstructive pulmonary
disease

- No requirement for supplemental oxygen

- No conditions that could result in excessive toxicity associated with the
benzodiazepine-like effects of MLN8237

- No inability to swallow oral medication or to maintain a fast as required for 2 hours
before and 1 hour after MLN8237 administration or any condition that would modify
small bowel absorption of oral medications, including malabsorption, or resection of
pancreas or upper bowel

- No patients with New York Heart Association (NYHA) Class II-IV heart failure

- See Disease Characteristics

- Last chemotherapy or radiation must be at least 4 weeks prior to enrollment on this
study

- Patients who decline other potentially curative therapy may be eligible

- Prior radiation therapy must not have been to more than 25% of the bone marrow

- Whole pelvic radiation is considered to be over 25%

- Prior allogeneic stem cell transplant patients will be allowed to enroll if they are
past day +100 of transplant, have no active graft-versus-host-disease, are not on any
immunosuppressants, and have been off immunosuppressants for at least 4 weeks

- Prior autologous stem cell transplant patients will be allowed to enter this study if
they are past their day +100 of transplant

- No patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for
nitrosoureas or mitomycin C) prior to entering the study or those who have not
recovered from adverse events due to agents administered more than 4 weeks earlier

- No patients who are receiving any other investigational agents

- No treatment with valproic acid within 14 days prior to initiation of study and
during the study

- No prior use of valproic acid or any other histone deacetylase (HDAC) inhibitor
for lymphoma treatment

- Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral
therapy are ineligible

- No requirement for constant administration of proton pump inhibitor, H2 antagonist,
or pancreatic enzymes

- Intermittent uses of antacids or H2 antagonists are allowed

- No treatment with clinically significant enzyme inducers, such as the enzyme-inducing
antiepileptic drugs phenytoin, carbamazepine, oxcarbazepine, primidone or
phenobarbital; rifampin, rifabutin, rifapentine; or St. John wort within 14 days
prior to the first dose of MLN8237 and during the study