This phase II trial will study the effectiveness of a combination regimen which includes Oncaspar (PEG-asparaginase), Doxil (PEG-liposomal doxorubicin), and Decadron (ODD) in terms of disease response against refractory lymphoid malignancies. Asparaginase is an enzyme that depletes asparagines, a key amino acid for survival and growth of malignant lymphocytes. Its depletion results in death of the neoplastic cell. Asparagine depletion has induced a significant improvement of clinical outcomes in acute lymphoblastic leukemia (ALL) and L-asparaginase has been a mainstay for more than 30 years in the treatment of ALL. Although this drug has been used primarily in ALL, promising results have been reported even in other non-ALL lymphoid malignancies, such as chronic lymphocytic leukemia (CLL), prolymphocytic leukemia, refractory non-Hodgkin's lymphoma (NHL) and multiple myeloma (MM). One of the main goals of this trial is to measure the asparaginase level as a surrogate marker of asparagine depletion with Oncaspar, a PEG-enhanced version of E. coli L-asparaginase. The therapeutic value of the simple, non-pegylated form of L-asparaginase is limited by its short half-life and propensity to cause allergic reactions.