Additional Study Information: This is a Phase 1 multicenter study of Vincristine Sulfate Liposome Injection (Marqibo) in combination with UK ALL R3 induction chemotherapy. The study treatment is considered experimental because it is not approved by the United States (US) Food and Drug Administration (FDA) for treating children with acute lymphoblastic leukemia (ALL) who have relapsed. The purpose of this study is to evaluate the toxicities and potential antitumor activity of Marqibo, given in combination with UK ALL R3 induction chemotherapy, in children with refractory ALL. Marqibo will be administered as an intravenous infusion over 60 minutes on days 1, 8, 15, and 22. Patients will receive UK ALL R3 induction chemotherapy which includes Dexamethasone (on days 1 to 5 and 15 to 19), Mitoxantrone (on days 1 and 2), PEG-asparaginase (on days 3 and 17), and intrathecal methotrexate (on days 1 and 8). Patients may receive only 1 cycle of therapy. In consenting patients, blood and bone marrow samples will be collected to evaluate the effects of Marqibo.