Inclusion Criteria:

          -  First 3 subjects: male and female subjects age ≥ 18 years and < 27 years

          -  Subsequent subjects: 12 months of age and <27 years of age at the time of study
             enrollment

          -  Disease status (one of the following):

               1. If post-allogeneic hematopoetic cell transplant (HCT): confirmed CD22+ leukemia
                  recurrence, defined as ≥0.01% disease

               2. If Relapse/Refractory status with no prior history of allogeneic HCT, one of:

                    -  2nd or grater marrow relapse, with or without extramedullary disease

                    -  1st marrow relapse at end of 1st month of re-induction with marrow having
                       ≥0.01% blasts by morphology and/or MPF

                    -  Primary Refractory, defined as >5% blasts by multi-parameter flow after ≥2
                       separate induction regimens

                    -  Subject has indication for HCT but is ineligible, inclusive of persistent
                       minimal residual disease

               3. CD22+ Lymphoma refractory or relapsed with no known curative therapies available

          -  Asymptomatic from CNS involvement, if present, and have a reasonable expectation that
             disease burden can be controlled in the interval between enrollment and T-cell
             infusion. Subjects with significant neurologic deterioration will not be eligible for
             T-cell infusion until stabilized.

          -  Free from active GVHD and off immunosuppressive GVHD therapy for 4 weeks.

          -  Lansky or Karnofsky performance score of ≥50

          -  Life expectancy of >8 weeks

          -  Recovered from acute toxic effects of all prior chemotherapy, immunotherapy, and
             radiotherapy

          -  ≥7 days post last chemotherapy administration (excluding intrathecal or maintenance
             chemotherapy)

          -  ≥7 days post last systemic corticosteroid administration

          -  No prior virotherapy

          -  Adequate organ function

          -  Adequate laboratory values

          -  Patients of childbearing/fathering potential must agree to use highly effective
             contraception

          -  Signed a written consent

        Exclusion Criteria:

          -  Presence of active clinically significant CNS dysfunction

          -  Pregnant or breastfeeding

          -  Unable to tolerate apheresis procedure, including placement of temporary apheresis
             line if required

          -  Presence of active malignancy other than CD22+ leukemia or lymphoma

          -  Presence of active severe infection

          -  Presence of any concurrent medical condition that would prevent the patient from
             undergoing protocol-based therapy

          -  Presence of primary immunodeficiency/bone marrow failure syndrome

          -  Unwilling to participate in 15-year follow-up period that is required if CAR T cell
             therapy is administered