This phase II trial is studying risk-directed therapy for B-lymphoblastic leukemia or lymphoma in first relapse. Standard risk (SR) and high risk (HR) participants will receive different therapy. Treatment will consist of chemotherapy for SR participants, and chemotherapy followed by hematopoietic stem cell transplant (HSCT) for HR in first relapse. Induction therapy consists of three blocks of chemotherapy. The first block is a novel immunotherapy regimen that includes chemotherapy, rituximab and infusion of haploidentical natural killer (NK) cells. SR participants will continue to receive chemotherapy for a total duration of approximately 2 years. HR participants will be candidates for HSCT and will proceed to transplant once a suitable donor is found and their minimal residual disease (MRD) is negative.