Inclusion Criteria:

* Age \>= 2 years
* Patient must have histologically confirmed primary mediastinal B-cell lymphoma (PMBCL) as defined by World Health Organization (WHO) criteria
* Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 or ECOG performance status of 3 if poor performance is related to lymphoma

* Children's Oncology Group (COG) Institutions: Use Karnofsky for patients \>= 17 and \< 18 years of age and Lansky for patients \< 17 years of age
* Adults (age 18 or older): Creatinine clearance \>= 30 mL/min, as estimated by the Cockcroft and Gault formula. The creatinine value used in the calculation must have been obtained within 28 days prior to registration. Estimated creatinine clearance is based on actual body weight
* Pediatric Patients (age \< 18 years): The following must have been obtained within 14 days prior to registration:

* Measured or calculated (based on institutional standard) creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 ml/min/1.73 m\^2, or
* Serum creatinine =\< 1.5 x institutional upper limit of normal (IULN), or a serum creatinine based on age/gender as follows:

* Age : 2 to \< 6 year; Maximum serum creatinine (mg/dL): 0.8 (male; 0.8 (female)
* Age : 6 to \< 10 years; Maximum serum creatinine (mg/dL): 1 (male); 1 (female)
* Age : 10 to \< 13 years; Maximum serum creatinine (mg/dL): 1.2 (male); 1.2 (female)
* Age : 13 to \< 16 years; Maximum serum creatinine (mg/dL): 1.5 (male); 1.4 (female)
* Age : \>= 16 years to \< 18 years; Maximum serum creatinine (mg/dL): 1.7 (male); 1.4 (female)
* Patients with abnormal liver function will be eligible to enroll if the lab abnormality is thought to be due to the lymphoma or Gilbert's syndrome
* Age \>= 18 years: Ejection fraction of \>= 50% by echocardiogram
* Age \< 18 years: Shortening fraction of \>= 27% by echocardiogram, or ejection fraction of \>= 50% by radionuclide angiogram
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
* Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
* All patients and/or their parents or legal guardians must sign a written informed consent
* All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met

Exclusion Criteria:

* Administration of prior anti-cancer therapy except as outlined below:

* A short course (=\< 2 weeks) of corticosteroids for the relief of lymphoma-related symptoms
* A single course of COP (cyclophosphamide, vincristine, and prednisone)
* One cycle of chemo-immunotherapy including R-CHOP, DA-EPOCH-R, a pediatric mature B-cell non-Hodgkin lymphoma (B-NHL) induction therapy (such as ANHL1131), or intrathecal chemotherapy that has not started more than 21 days prior to enrollment
* Active ischemic heart disease or heart failure
* Active uncontrolled infection
* Central nervous system (CNS) involvement of lymphoma
* Patients with a prior or concurrent malignancy whose natural history or treatment has the potential to interfere with safety or efficacy assessment of this trial
* Active autoimmune disease that has required systemic treatment (such as disease modifying agents, corticosteroids, or immunosuppressive agents) in the past 2 years. Replacement therapy such as thyroxine, insulin or physiologic corticosteroid for adrenal or pituitary insufficiency is not considered a form of systemic treatment
* In patients \< 18 years of age hepatitis B serologies consistent with past or current infections
* Patients with severe hepatic impairment (Child-Pugh class C or serum total bilirubin \> 5.0 mg/dL) unless thought to be due to lymphoma or Gilbert's syndrome
* Female patients who are pregnant since fetal toxicities and teratogenic effects have been noted for several of the study drugs. A pregnancy test is required for female patients of childbearing potential
* Sexually active patients of reproductive potential who have not agreed to use a highly effective contraceptive method (failure rate of \< 1% per year when used consistently and correctly) for the duration of their study participation
* Lactating females are not eligible unless they have agreed not to breastfeed their infants starting with the first dose of study therapy and for at least 6 months after the last dose of rituximab