Combination Chemotherapy, Rituximab, and Ixazomib Citrate in Treating Patients With Non-Hodgkin Lymphoma

Inclusion Criteria:

* Patients must have a histological diagnosis of any of the following (all stages allowed):

  * Diffuse large b-cell lymphoma (DLBCL) (including transformation from a previously indolent non-Hodgkin lymphoma \[NHL\], so long as no prior systemic treatment was given for the indolent NHL)
  * B-cell lymphoma, unclassifiable, with features intermediate between diffuse large B-cell lymphoma
  * Burkitt lymphoma
  * MYC+ plasmablastic lymphoma by histology
* Patients must have measurable disease (defined as \>= 1.5 cm in diameter)
* Patients must have MYC-rearrangement, as determined by fluorescent in-situ hybridization (FISH) (does not require central review)
* The following results must be available or pending at time of registration, though results will not affect enrollment/treatment:

  * B-cell chronic lymphocytic leukemia (CLL)/lymphoma (BCL)-2 rearrangement by FISH
  * BCL-6 rearrangement by FISH NOTE: although not required, it is encouraged that MYC and BCL-2 be measured by immunohistochemistry (IHC) and clearly documented
* Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of 0-3
* Absolute neutrophil count (ANC) \>= 1,000/mm\^3
* Platelets \>= 75,000/mm\^3
* Total bilirubin =\< 1.5 x upper limit of normal (ULN); NOTE: exceptions can be granted from principal investigator (PI) for instances of Gilbert's disease, and/or primarily indirect bilirubinemia, if due to recent transfusion and/or hemolysis
* Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase \[SPGT\]) =\< 3 X institutional ULN
* Calculated creatinine clearance \>= 30 mL/min
* NOTE: platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before registration; these requirements do not apply to those with marrow involvement of lymphoma (any extent)
* Female patients must meet one of the following criteria:

  * Postmenopausal for at least 1 year prior to registration
  * Surgically sterile
  * Of childbearing potential and agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug
  * Of childbearing potential and agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject NOTE: periodic abstinence (eg, calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception
* Male patients, even if surgically sterilized (ie, status post-vasectomy), must agree to one of the following:

  * Agree to practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug
  * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject NOTE: periodic abstinence (eg, calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception
* Females of child-bearing potential (FOCBP) must have a negative pregnancy test within # days prior to registration on study
* Patients must have the ability to understand and the willingness to sign a written informed consent prior to registration on study

Exclusion Criteria:

* Patients who have had more than one cycle of prior chemoimmunotherapy for diagnosis of NHL are not eligible; NOTE: such patients must have fully recovered (ie, =\< grade 1 toxicity) from the reversible effects of prior chemotherapy before starting treatment on the current protocol
* Patients who have had major surgery within 4 weeks prior to registration are not eligible
* Patients who have had radiotherapy within 14 days before registration are not eligible; NOTE: If the involved field is small, 7 days will be considered a sufficient interval between treatment and administration of the ixazomib
* Patients who have an infection requiring systemic antibiotic therapy or other serious infection within 14 days before study enrollment are not eligible
* Patients who have evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, uncontrolled cardiac arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial infarction within the past 6 months are not eligible
* Patients who have undergone systemic treatment, within 14 days prior to registration, with strong inhibitors of cytochrome P450 superfamily (CYP)1A2 (fluvoxamine, enoxacin, ciprofloxacin), strong inhibitors of CYP3A (clarithromycin, telithromycin, itraconazole, voriconazole, ketoconazole, nefazodone, posaconazole) or strong CYP3A inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or use of Ginkgo biloba or St. John's wort are not eligible
* Patients who have a clinically active hepatitis B or C virus infection are not eligible; NOTE: those with evidence of exposure to hepatitis B virus (HBV) may enroll so long as HBV viral load is negative AND subject is willing/able to take appropriate antiviral prophylaxis to prevent reactivation
* Patients with any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol are not eligible
* Patients who have a known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent are not eligible
* Patients who have a known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of ixazomib including difficulty swallowing are not eligible
* Patients who have been diagnosed or treated for another malignancy within 2 years before study enrollment or previously diagnosed with another malignancy and have any evidence of residual disease are not eligible; NOTE: Patients with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection
* Patients who have \>= grade 3 peripheral neuropathy, or grade 2 with pain on clinical examination during the screening period are not eligible
* Patients who are participating in other clinical trials, including those with other investigational agents not included in this trial, within 30 days of registration and throughout the duration of this trial are not eligible
* Female patients who are nursing or have a positive pregnancy test during screening are not eligible