A safety/activity phase is conducted separately for the intermediate-risk (IR) and high-risk (HR) patients to identify a safe, tolerable, and biologically active dose of lestaurtinib combined with chemotherapy backbone. Once a tolerable/active dose of lestaurtinib has been identified for IR patients, subsequent IR patients are eligible to proceed to an efficacy phase, where they are randomized (or non-randomly assigned as of 7/16/2014) to chemotherapy with or without lestaurtinib. HR patients separately proceed to the randomized efficacy phase if a tolerable/active dose is identified for the HR stratum. IR and HR patients are randomized (or non-randomly assigned as of 7/16/2014) to 1 of 2 post-induction therapy regimens (post-induction therapy B or C).