Inotuzumab Ozogamicin in Treating Younger Patients With B-Lymphoblastic Lymphoma or Relapsed or Refractory CD22 Positive B Acute Lymphoblastic Leukemia

Inclusion Criteria: * Patients must be \>= 1 year and \< 22 years of age at the time of enrollment * Patients must have B-ALL, or previously diagnosed B lymphoblastic lymphoma (B-LL), with \>= 5% (M2 or M3) bone marrow blasts with or without extramedullary disease * NOTE: Relapsed patients previously diagnosed with B-lymphoblastic lymphoma (B-LL) are eligible if they have an M2 or M3 marrow at the time of enrollment on this study * Patients with ALL or B-LL who have M2 morphology must have local confirmatory testing showing \>= 5% blasts by flow cytometry, fluorescence in situ hybridization (FISH) testing or other molecular method * Leukemic blasts must demonstrate surface expression of CD22 at the time of relapse by local/institutional flow cytometry of a bone marrow aspirate sample; (assessment of CD22 using a bright fluorophore such as phycoerythrin \[PE\] is strongly recommended) * In the case of an inadequate aspirate sample (dry tap) or if bone marrow aspirate is unable to be performed due to patient clinical status, flow cytometry of peripheral blood specimen may be substituted if the patient has at least 1,000/uL circulating blasts; alternatively, CD22 expression may be documented by immunohistochemistry of a bone marrow biopsy specimen * Patients with one of the following: * Second or greater relapse; * Primary refractory disease with at least 2 prior induction attempts; * First relapse refractory to at least one prior re-induction attempt * Any relap…