Dose Adjusted EPOCH Regimen in Combination With Ofatumumab or Rituximab in Treating Patients With Newly Diagnosed or Relapsed or Refractory Burkitt Lymphoma or Relapsed or Refractory Acute Lymphoblastic Leukemia

Inclusion Criteria:

* Burkitt's or Burkitt-like leukemia/lymphoma, either previously untreated, or relapsed/refractory, or human immunodeficiency virus (HIV)-related; patients with double or triple hit high-grade leukemia/lymphoma are eligible also; patients HIV positive will be described and reported separately or relapsed/refractory acute lymphoblastic leukemia (ALL).
* Zubrod performance status =\< 3 (Eastern Cooperative Oncology Group \[ECOG\] scale)
* Creatinine less than or equal to 2.0 mg/dL (unless considered tumor related)
* Bilirubin less than or equal to 2.0 mg/dL (unless considered tumor related)
* Adequate cardiac function defined as no history of clinically significant arrhythmia, or history of myocardial infarction (MI) within 3 months prior to study enrollment; cardiac function will be assessed by history and physical examination

Exclusion Criteria:

* Pregnant or nursing women
* Active and uncontrolled disease/infection as judged by the treating physician
* Unable or unwilling to sign the consent form
* Subjects who have current active hepatic or biliary disease (with exception of patients with Gilbert's syndrome, asymptomatic gallstones, liver metastases or stable chronic liver disease per investigator assessment)