This is an open-label, dose-escalation Phase I study of ON 013105 in patients with relapsed/refractory Lymphoma or B-cell Acute Lymphocytic Leukemia (Philadelphia chromosome negative) who have satisfied all inclusion/exclusion criteria. Patients will receive weekly 2-hour IV infusions of ON 013105, until evidence of disease progression, intolerable adverse events, or withdrawal of patient consent. Up to 12 additional patients will be treated at the RPTD level. The starting dose will be 17 mg over a 2-hour weekly infusion. Each cycle will comprise three weeks.