Doxorubicin Hydrochloride Liposome and Rituximab With Combination Chemotherapy in Treating Patients With Newly Diagnosed Burkitt's Lymphoma or Burkitt-Like Lymphoma

DISEASE CHARACTERISTICS: * Histologically confirmed Burkitt's or Burkitt-like non-Hodgkin's lymphoma meeting 1 of the following risk criteria: * Low-risk disease meeting all of the following criteria: * Normal lactate dehydrogenase level * ECOG performance status 0-1 * Ann Arbor stage I or II * No tumor mass over 10 cm in greatest diameter * High-risk disease, defined as disease not meeting low-risk criteria * Newly diagnosed disease PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * Hemoglobin ≥ 8.0 g/dL * Absolute neutrophil count ≥ 500/mm³ * Platelet count ≥ 100,000/mm³ (50,000/mm³ if bone marrow involvement is documented) * AST and ALT ≤ 3 times upper limit of normal (ULN) * Alkaline phosphatase ≤ 3 times ULN * Bilirubin ≤ 1.5 times ULN (3 times ULN if liver metastases are present) * Creatinine clearance \> 50 mL/min * Creatinine ≤ 2.0 mg/dL * LVEF ≥ 45% by MUGA scan or echocardiogram * No New York Heart Association class II-IV heart failure * No clinically significant pericardial disease * No myocardial infarction within the past 6 months * No uncontrolled angina * No severe uncontrolled ventricular arrhythmias * No ECG evidence of acute ischemia or active conduction system abnormalities * Investigator must document any baseline ECG abnormality as not medically relevant * No other malignancy within the past year except for basal cell c…