Testing the Combination of Inotuzumab Ozogamicin and Lower Dose Chemotherapy Compared to Usual Chemotherapy for Adults With B-Cell Acute Lymphoblastic Leukemia or B-Cell Lymphoblastic Lymphoma

Inclusion Criteria:

   - PRE-REGISTRATION ELIGIBILITY CRITERIA (STEP 0)

   - Research bone marrow or peripheral blood submission

   * This bone marrow or peripheral blood submission is mandatory prior to
   registration/randomization as baseline for real-time MRD analysis. The bone marrow
   sample should be from the first aspiration (i.e., first pull). Aspirate needle should
   be redirected if needed to get first pull bone marrow aspirate. It should be obtained
   as soon after pre-registration as possible

   - REGISTRATION INCLUSION CRITERIA (STEP 1)

   - Diagnosis of B-cell acute lymphoblastic leukemia (ALL) or lymphoblastic lymphoma (LBL)
   per World Health Organization (WHO) 2016 criteria. Patients must have >= 5% blasts in
   the bone marrow or blood. Patients with lymphoblastic lymphoma (LBL) without
   measurable marrow involvement (>= 5% blasts) are not eligible

   * T-cell ALL/LBL, Philadelphia-chromosome positive B-cell (as determined by
   fluorescence in situ hybridization [FISH], cytogenetics, or reverse transcriptase
   polymerase chain reaction [RT-PCR]), and Burkitt's like leukemia/lymphoma (mature
   B-ALL) are not eligible

   - Must be CD22 positive by local assessment (>= 20% by immunohistochemistry or flow
   cytometry). Patients are eligible regardless of CD20 status but CD20 expression should
   be assessed at diagnosis by flow cytometry or immunohistochemistry

   - Patients must have >= 5% blasts in the bone marrow or blood. Patients with
   lymphoblastic lymphoma (LBL) without marrow involvement (>= 5% blasts) are not
   eligible

   - No prior chemotherapy for ALL except for hydroxyurea (no limit), steroids limited to 7
   days, ATRA (no limit), vincristine (single dose), and/or intra-thecal chemotherapy.
   Leukapheresis is permitted. Palliative radiation to doses 24 Gy or less is permitted.
   Patients being treated with chronic steroids for other reasons (autoimmune disorder,
   etc.) are eligible

   - Age >= 50 years

   - Eastern Cooperative Oncology Group (ECOG) performance status =< 2. ECOG 3 permitted if
   related to disease

   - Creatinine =< 2.0 g/dL

   - Total bilirubin =< 1.5 x upper limit of normal (ULN)

   * Except in the event of: 1) Gilbert disease, in which case total bilirubin must be =<
   2 x ULN, or 2) elevated bilirubin believed by investigator to be due to leukemic
   infiltration, in which case total bilirubin must be =< 2 x ULN

   - AST / ALT =< 2.5 x upper limit of normal (ULN)

   - Cardiac ejection fraction (as measured by multigated acquisition scan [MUGA] or
   echocardiogram) > 40%

   - No clinically relevant liver disease (such as cirrhosis, active hepatitis, or alcohol
   use disorder), which in the opinion of the treating physician would make this protocol
   unreasonably hazardous

      - Patients with known hepatitis B virus (HBV) infection are eligible if they are on
      effective HBV suppressive therapy with undetectable HBV viral load and there is
      no clinically relevant liver disease present (related or unrelated to HBV-related
      liver damage)

      - Patients with known history of hepatitis C virus (HCV) infection are eligible if
      they have cleared the infection spontaneously or via eradication therapy (HCV
      viral load undetectable) and there is no clinically relevant liver disease
      present (related or unrelated to HCV-related liver damage)

   - Women and men of reproductive potential should agree to use an appropriate method of
   birth control throughout their participation in this study due to the teratogenic
   potential of the therapy utilized in this trial. Include as applicable: Appropriate
   methods of birth control include abstinence, oral contraceptives, implantable hormonal
   contraceptives, or double barrier method (diaphragm plus condom)

Exclusion Criteria:

   - Physicians should consider whether any of the following may render the patient
   inappropriate for this protocol:

      - Medical condition such as uncontrolled diabetes mellitus, uncontrolled cardiac
      disease, and uncontrolled pulmonary disease.

      - Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
      therapy with undetectable viral load within 6 months are eligible for this trial.

      - Patients with a "currently active" second malignancy other than non-melanoma skin
      cancers, early stage prostate cancer, cervical carcinoma in situ, or other cancer
      for which standard of care would be observation (not requiring treatment).
      Patients are not considered to have a "currently active" malignancy if they have
      completed therapy and are free of disease for >= 1 year, or if the cancer has
      been surgically resected and considered cured. Patients with a history of
      multiple myeloma with absence of serum paraprotein for >= 1 year are not
      considered to have a "currently active" malignancy.

   - REGISTRATION EXCLUSION CRITERIA (STEP 1)

   - Patients with symptomatic central nervous system (CNS) disease are not eligible. CNS
   assessment is not required for eligibility determination if asymptomatic