Rituximab and Combination Chemotherapy in Treating Patients With Previously Untreated High- or High-Intermediate-Risk Diffuse Large B-Cell Lymphoma

Inclusion Criteria: * Newly diagnosed cluster of differentiation (CD) 20+ DLBCL with IPI between 3-5 * No prior chemotherapy, radiation therapy or immunotherapy for DLBCL; a short course (\< 2 weeks) of corticosteroids is allowed for symptom control Signed informed consent * Eastern Cooperative Oncology Group (ECOG) Performance status assessed between 0 and 2; performance status of 3 will be accepted if impairment is caused by DLBCL complications and improvement is expected once therapy is initiated * Measurable disease by Non-Hodgkin's Lymphoma Response Criteria on FDG-PET/CT; baseline measurements and evaluations must be obtained =\< 21 days prior to registration * Absolute neutrophil count (ANC) \>= 1,500/μL unless due to marrow involvement by lymphoma * Platelets \>= 75,000/μL unless due to marrow involvement by lymphoma Hemoglobin \> 7.0 g/dL unless due to marrow involvement by lymphoma * Creatinine =\< 2.0 mg/dL or calculated creatinine clearance \>= 40 * Total bilirubin =\< 1.5 mg/dL unless due to Gilbert's disease * Aspartate aminotransferase (AST)/ alanine aminotransferase (ALT) =\< 2.5 the upper limit of normal * Alkaline phosphatase =\< 5x upper limit of normal * Patients with bilirubin between 1.5-3.0 mg/dL due to lymphoma may be entered and doses adjusted * Left ventricular ejection fraction (LVEF) \>= 50% Exclusion Criteria: * Women who are pregnant or breast feeding * Known seropositivity for human immunodeficiency virus (HIV) * Known presence of central nervous system (CNS) involvement by lymphoma * New York Heart Association Classification III or IV heart * Current or chronic hepatitis B or hepatitis C infection (as detected by positive testing for Hepatitis B surface Antigen \[Hbs Ag\] or antibody to Hepatitis C virus \[anti HCV\] respectively); patients must be tested for Hepatitis B surface antigen and anti-HCV =\< 21 days prior to registration * Male patients (with female sexual partners of childbearing potential) and female patients of childbearing potential who refuse to use effective methods of contraception * Unstable or severe uncontrolled medical, psychological, or social condition * Any evidence of serious active, uncontrolled infection (i.e., requiring an IV antibiotic or antiviral agent) * Receipt of live vaccine within 4 weeks prior to study drug administration * Concurrent active malignancy other than non-melanoma skin cancer or carcinoma in situ of the cervix; subjects with previous malignancies are eligible provided that they have been treated with curative intent and remain disease free for 3 years or more * No prior chemotherapy for lymphoma * Prior radiation therapy for lymphoma * Any important medical illness or abnormal laboratory finding that would, in the investigator's judgment, significantly increase the subject's risk of participating in this study