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

You may be eligible if

• 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