Inclusion Criteria -

          1. Between the ages of greater or equal to (≥) 6 months and less than (<) 18 years of age

          2. Must have histologically proven B-cell acute lymphoblastic leukemia (ALL) or B-cell
             lymphoblastic lymphoma with marrow involvement

          3. All participants (both ALL and participants with lymphoblastic lymphoma) must have M2
             or M3 bone marrow classification

          4. Disease status: a) Participants must have relapsed or refractory disease b) In the
             event of relapse after prior allogeneic hematopoietic stem cell transplant (HSCT),
             participants must be at least 3 months post-transplant and have no evidence of active
             graft-vs-host disease, and must have been off immunosuppression for at least 4 weeks,
             c) Must have resolution of the acute toxic effects to less than or equal to (≤) Grade
             2 from prior chemotherapy before entry, in the opinion of the investigator

          5. Participants with the following central nervous system (CNS) 1 or 2 status are
             eligible only in the absence of neurologic symptoms

          6. Female participants of childbearing potential and post-pubertal male participants must
             use an approved method of contraception for the study.

        Exclusion Criteria

          1. Concurrent enrollment in another clinical study for cancer treatment, unless the
             subject is in the follow-up period from a previous study.

          2. Isolated testicular or CNS ALL

          3. Participants with mixed-lineage leukemia (MLL) gene rearrangement

          4. Inadequate Hepatic function

          5. Inadequate Renal function

          6. Radiologically-detected CNS lymphoma

          7. Participants with clear laboratory or clinical evidence of disseminated intravascular
             coagulation (DIC)

          8. Hyperleukocytosis or rapidly progressive disease that would compromise ability to
             complete study therapy

          9. QT interval corrected using Fridericia's formula (QTcF) greater than or equal to a
             Grade 2, confirmed by 2 additional seperate electrocardiographs (ECG's) within 28 days
             prior to starting study drug. The initial screening ECG need not be repeated for
             confirmation if the QTcF interval is <481 milliseconds.

         10. Pregnant or breast-feeding females

         11. Prior treatment with CAT-3888 (BL22), moxetumomab pasudotox, or any
             pseudomonas-exotoxin-containing compound

         12. Prior treatment with any anticancer biologic therapy within 2 weeks prior to starting
             study drug, including but not limited to therapeutic monoclonal antibodies or
             antibody-drug conjugates

         13. Systemic chemotherapy ≤ 2 weeks (6 weeks for nitrosoureas) and radiation therapy ≤ 3
             weeks prior to starting study drug

         14. Clinically significant ophthalmologic findings (evidence of retinal damage or injury)
             during the screening

         15. Presence of a second invasive malignancy

         16. Uncontrolled pulmonary infection, presence of pulmonary edema

         17. Serum albumin < 2 gram per deciliter (g/dL). Albumin infusions for correction of
             hypoalbuminemia are allowed, but cannot have administered within 7 days prior to start
             of study drug

         18. Radioimmunotherapy within 2 years prior to study start of study drug

         19. Participants with prior history of thrombotic microangiopathy or hemolytic uremic
             syndrome (HUS)

         20. T-cell ALL or T-cell lymphoblastic lymphoma

         21. Participants currently receiving high-dose estrogen therapy defined as >0.625
             milligram per day (mg/day) of an estrogen compound or within 2 weeks prior to starting
             study drug.