Alisertib With and Without Rituximab in Treating Patients With Relapsed or Refractory B-Cell Non-Hodgkin Lymphoma

Inclusion Criteria:

* Must have histologically proven relapsed or refractory B-cell NHL of the following World Health Organization (WHO) classification subtypes: follicular lymphoma (FL), mantle cell lymphoma (MCL), lymphoplasmacytic lymphoma/Waldenström's macroglobulinemia (LPL/WM), marginal zone lymphoma (MZL), diffuse large B-cell lymphoma (DLBCL), Burkitt's lymphoma (BL), and B-cell lymphoma with features unclassifiable between Burkitt's and large cell lymphoma; alternatively, patients with histologically proven, newly diagnosed transformed non-Hodgkin's lymphoma (tNHL) are eligible
* Eastern Cooperative Oncology Group (ECOG) performance status 0-2
* At least one prior therapy; patients with newly diagnosed tNHL are eligible and do not need to have received prior therapy for the transformed lymphoma or prior indolent NHL; prior autologous stem cell transplant is allowed
* Serum creatinine =\< 2.0 mg/dL
* Total bilirubin within normal limits
* Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 1.5 x upper limit of normal
* Absolute neutrophil count (ANC) \>= 1000/μL
* Platelet count \>= 75,000/μL
* Recovery to =\< grade 1 toxicities associated with prior therapy
* 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performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care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 subject agrees to use an acceptable method for contraception during the entire study treatment period through 4 months after the last dose of MLN8237
* Must be able to take oral medication and to maintain a fast as required for 2 hours before and 1 hour after MLN8237 administration

Exclusion Criteria:

* Pregnant or breast-feeding women and women of childbearing age who are unwilling to use adequate contraception
* Patients with a history of central nervous system involvement by lymphoma
* Patients with known human immunodeficiency virus (HIV), hepatitis B or hepatitis C (active or carriers) are not eligible; this includes all patients with a positive hepatitis C antibody, hepatitis B surface antigen, or hepatitis B core antibody; previously vaccinated patients with positive hepatitis B surface antibody are eligible
* May not have received prior therapy with an Aurora kinase inhibitor
* Patients eligible for and willing to undergo autologous stem cell transplant with curative intent at the time of enrollment are not eligible; patients refractory to at least 2 prior regimens may enroll and proceed to curative autologous transplant if they respond
* Patients who are on chronic steroids for unrelated conditions (i.e. rheumatologic conditions) are not eligible if their total daily dose of steroids is equivalent to greater than 10 mg prednisone
* Radiation therapy to more than 25% of the bone marrow; whole pelvic radiation is considered to be over 25%
* Prior allogeneic bone marrow or organ transplantation
* If applicable, patient has \>= grade 2 peripheral neuropathy within 14 days before enrollment
* Known history of uncontrolled sleep apnea syndrome and other conditions that could result in excessive daytime sleepiness, such as severe chronic obstructive pulmonary disease; requirement for supplemental oxygen
* Patients who are on daily proton pump inhibitor therapy must be able to discontinue use or only require use of antacid or hydrogen (H2) antagonist intermittently; patients who require daily administration of proton pump inhibitor, H2 antagonist, or pancreatic enzymes are not eligible; intermittent uses of antacids or H2 antagonists are allowed
* Systemic infection requiring IV antibiotic therapy within 14 days preceding the first dose of study drug, or other severe infection
* 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 (except asymptomatic patients with a pacemaker with electrocardiogram (ECG) changes reflecting conduction abnormalities secondary to the pacemaker); prior to study entry, any ECG abnormality at screening has to be documented by the investigator as not medically relevant
* Female subject is pregnant or breast-feeding; confirmation that the subject is not pregnant must be established by a negative serum β-human chorionic gonadotropin (β-hCG) pregnancy test result obtained during screening; pregnancy testing is not required for post-menopausal or surgically sterilized women
* Patient has received other investigational drugs with 14 days before enrollment
* Serious medical or psychiatric illness likely to interfere with participation in this clinical study
* Other severe acute or chronic medical or psychiatric condition, including uncontrolled diabetes, malabsorption, resection of the pancreas or upper small bowel, requirement for pancreatic enzymes, any condition that would modify small bowel absorption of oral medications, or laboratory abnormality that may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for enrollment in this 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
* Treatment with clinically significant enzyme inducers, such as the enzyme- inducing antiepileptic drugs phenytoin, carbamazepine or phenobarbital, or rifampin, rifabutin, rifapentine or St. John's wort within 14 days prior to the first dose of MLN8237 and during the study
* Patients with a corrected QT interval (QTc) at baseline of \> 450 milliseconds or other factors that increase the risk of QT prolongation or arrhythmic events (i.e., heart failure, hypokalemia with potassium \< 3.5 despite supplementation, family history of long QT syndrome) should be excluded
* Patients who require use of a concomitant medication that can prolong the QT interval and who are unable to discontinue use of this medication during the study period are excluded