Eligible candidates will be adults with aggressive or very aggressive NHL (WHO classification diagnosis confirmed by histological tumor examination). Patients must have failed one or more prior NHL chemotherapy or antibody therapy with curative intent, and the disease must not have progressed within 60 days of last therapy. In addition, patients must not be candidates for potentially curative therapy, such as HSCT, or they must have refused these alternative therapies. Full inclusion/exclusion criteria are available. History and physical examination, and laboratory and imaging analyses will be done within 14 days prior to registration. Intravenous ascorbic acid will be given in a dose based on the plasma vitamin C level to reach a level in the range of 300 to 350 mg/dL. Vitamin C infusions will be given three times a week on a schedule that allows at least 24 hours between each infusion, for a total of ten weeks (30 infusions). If disease progression occurs before or at the ten week assessment, then we discontinue protocol, based on futility. Toxicity and adverse events also will result in immediate discontinuation (details available in full protocol). If there is lack of disease progression or disease improvement, proceed and reassess again at 10 week intervals, for a total of three 10 week intervals. Initial criteria are based upon the criteria from the International Workshop to Standardize Criteria for Non-Hodgkin's Lymphoma (Cheson et al., Report of an international workshop to standardize response criteria for non-Hodgkin's lymphoma, Journal of Clinical Oncology, 1999, Vol. 17, No4, 1244-1253); response for this study will utilize PET in accordance with revised criteria (Cheson et al. Revised response criteria for malignant lymphoma. J of Clin Oncol 2007; 25(5): 579-586). We select 20 patients as an appropriate study size to evaluate a true response rate to therapy, compared to just the observed response.