• 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/sex 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 : \>= 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