Pegylated Liposomal Doxorubicin (Doxil) With Rituximab in Relapsed AIDS-Related Non-Hodgkin's Lymphomas

Inclusion Criteria: * Histologically or cytologically documented B-cell non-Hodgkin's lymphoma \[NHL\] (diffuse mixed, diffuse or follicular large B-cell, immunoblastic), Burkitt or Burkitt-like lymphomas, and primary effusion lymphomas. * Seropositive for HIV by any approved test (prior documentation of HIV seropositivity is acceptable). * Failed or relapsed after at least 1 prior chemotherapy treatment (chemotx) regimen but could have had no more than 2 prior chemotx regimens with only one of them being an anthracycline-containing regimen. Prior treatment (tx) with rituximab allowed. * All stages of disease * Measurable or evaluable tumor * Greater than or equal to 18 years of age * Karnofsky performance status greater than 50% * Absolute granulocyte count (AGC) greater than 1.0; platelets greater than 75,000; hemoglobin (Hgb) greater than 8.0 (unless these parameters are abnormal secondary to lymphomatous involvement of marrow, or due to HIV-related thrombocytopenia). * Bilirubin less than 2.0 (unless elevated secondary to lymphomatous involvement of liver or biliary system or due to other HIV-related medications such as Crixivan). * Creatinine less than 2.5 or creatinine clearance greater than 60 ml/min * Multigated acquisition (MUGA) scan or 2D echocardiogram indicating left ventricular ejection fraction (LVEF) greater than or equal to 50% within 42 days prior to first dose of study drug. * Patients with central nervous system (CNS) involvement are eligible provided that systemic lymphomatous disease is also present. * Concurrent therapy for HIV with any licensed agent or an agent available on an expanded access program will be required. * Signed informed consent including Health Insurance Portability and Accountability Act of 1996 (HIPAA) authorization. Exclusion Criteria: * Acute intercurrent infection that may interfere with planned protocol. Patients with mycobacterium avium are not excluded. Chronic therapy with potentially myelosuppressive agents is allowed provided that entry hematologic criteria are met. * Second active tumor. Patients with non-melanomatous skin cancer, in-situ cervical cancer, or Kaposi's sarcoma, not requiring systemic chemotherapy may be entered on study. * Primary CNS lymphoma. * Documented history of congestive heart failure (CHF), hemodynamically unstable arrhythmia, myocardial infarction (MI) in the preceding 6 months, or evidence on electrocardiogram (EKG) of untreated cardiac ischemia. * Prior exposure to a liposomal anthracycline (liposomal doxorubicin or daunorubicin) for the treatment of lymphoma. Prior exposure to conventional doxorubicin allowed. * Prior radiation therapy within 4 weeks, unless for emergency conditions secondary to lymphoma (i.e., CNS tumor, cord compression) * Prior systemic chemotherapy or biologic therapy within 3 weeks * History of hypersensitivity reaction to anthracyclines or granulocyte colony-stimulating factor (G-CSF) * History of hypersensitivity reactions attributed to a conventional formulation of doxorubicin hydrochloride (HCl) * Investigational agent(s) within 4 weeks of start of study therapy. * History of cardiac disease with New York Heart Association (NYHA) greater than or equal to Class II, or clinical evidence of CHF * Pregnant or nursing mothers.