INCLUSION CRITERIA:

          1. Disease Status Disease Status of ALL

               -  Must have chemotherapy refractory disease defined as progression or stable
                  disease after two lines of therapies, or

               -  Relapsed disease after achieving CR.

               -  Subjects with persistent or relapsed minimal residual disease (MRD) (by flow
                  cytometry, PCR, fluorescence in situ hybridization (FISH), or next generation
                  sequencing (NGS) require verification of MRD on two occasions at least 2 weeks
                  apart.

               -  Subjects with Philadelphia Chromosome positive acute lymphoblastic leukemia
                  (Ph+ALL) subjects are eligible if they progressed, had stable disease or relapsed
                  after two lines of therapy, including tyrosine kinase inhibitors (TKIs).

               -  Subjects with recurrence of isolated central nervous system CNS) relapse after
                  achieving complete remission (CR).

             Disease Status of lymphoma

               -  Histologically confirmed aggressive B cell NHL including the following types
                  defined by WHO 2008:

                  - DLBCL not otherwise specified; T cell/histiocyte rich large B cell lymphoma;
                  DLBCL associated with chronic inflammation; Epstein Barr virus (EBV)+ DLBCL of
                  the elderly; OR primary mediastinal (thymic) large B cell lymphoma transformation
                  of follicular lymphoma, marginal zone lymphoma or chronic lymphocytic
                  leukemia/small lymphocytic lymphoma to DLBCL will also be included

               -  Subjects with DLBCL must have progressed, had SD, or recurred after initial
                  treatment regimens that include an anthracycline and an anti CD20 monoclonal
                  antibody. Subjects with transformed Follicular lymphoma(FL), marginal zone B-cell
                  lymphoma (MZL), or chronic lymphocytic leukemia/small lymphocytic lymphoma
                  (CLL/SLL) must have progressed, had SD, or recurred with transformed disease
                  after initial treatment for DLBCL. Subjects who relapse ≥12 months after therapy
                  should have progressed after autologous transplant or been ineligible for
                  autologous transplant.

          2. Measureable Disease

               -  Subjects with ALL must have evaluable or measurable disease.

               -  Subjects with lymphoma: Must have evaluable or measurable disease according to
                  the revisedInternational Working. Group( IWG) Response Criteria for Malignant
                  Lymphoma. Lesions that have been previously irradiated will be considered
                  measurable only if progression has been documented following completion of
                  radiation therapy.

          3. CD22 expression

             • Subjects with ALL: CD22 positive expression on malignant cells is required and must
             be detected by immunohistochemistry or by flow cytometry. The choice of whether to use
             flow cytometry or immunohistochemistry will be determined by what is the most easily
             available tissue sample in each subject.

             CD22 expression must be demonstrated subsequent to any anti-CD22 targeted therapy
             (e.g. Moxetumomab pasudotox or inotuzumab ozogamicin) in subjects with ALL

             • Subjects with lymphoma: must have archival tissue available for analysis of CD22
             expression, or must be willing to undergo a biopsy of easily accessible disease.

          4. Prior Bone Marrow-Stem Cell Transplant Subjects who have undergone autologous stem
             cell transplant (SCT) with disease progression or relapse following SCT are eligible.
             Subjects who have undergone allogeneic SCT will be eligible if, in addition to meeting
             other eligibility criteria, they are at least 100 days post transplant, they have no
             evidence of Graft versus host disease (GVHD) and have been without immunosuppressive
             agents for at least 30 days.

          5. Prior Therapy Wash-out

               -  At least 2 weeks or 5 half lives, whichever is shorter, must have elapsed since
                  any prior systemic therapy at the time the subject is planned for leukapheresis,
                  except for systemic inhibitory/stimulatory immune checkpoint therapy, which
                  requires 5 half lives.

               -  Subjects with ALL may not have receive inotuzumab ozogamicin therapy within the
                  past 4 months.

             Exceptions:

               -  There is no time restriction with regard to prior intrathecal chemotherapy
                  provided there is complete recovery from any acute toxic effects of such;

               -  Subjects receiving hydroxyurea may be enrolled provided there has been no
                  increase in dose for at least 2 weeks prior to starting apheresis;

               -  Subjects who are on standard ALL maintenance type chemotherapy (vincristine, 6-
                  mercaptopurine or oral methotrexate) may be enrolled provided that chemotherapy
                  is discontinued at least 1 week or 5 half-lives, whichever is shorter,prior to
                  apheresis.

               -  Subjects receiving steroid therapy at physiologic replacement doses (≤ 5 mg/day
                  of prednisone or equivalent doses of other corticosteroids) only are allowed
                  provided there has been no increase in dose for at least 2 weeks prior to
                  starting apheresis;

               -  For radiation therapy: Radiation therapy must have been completed at least 3
                  weeks prior to enrollment, with the exception that there is no time restriction
                  if the volume of bone marrow treated is less than 10% and also the subject has
                  measurable/evaluable disease outside the radiation port or the site of radiation
                  has documented progression.

          6. Prior CAR Therapy Subjects who have undergone prior CAR therapy will be eligible if at
             least 30 days has elapsed prior to apheresis.

          7. Toxicities from Prior Therapy Toxicities due to prior therapy must be stable (except
             for clinically non significant toxicities such as alopecia)

          8. Age greater than or equal to 1 year and ≤ 30 years of age at time of enrollment. First
             3 subjects treated at the dose level must be at least 16 years old (enrolled on either
             pediatric or adult protocol).

          9. Performance Status:

             Subjects > 10 years of age: Karnofsky ≥ 70% OR Eastern cooperative oncology group
             (ECOG) performance status of 0 or 1; Subjects ≤ 10 years of age: Lansky scale ≥ 70%

         10. Normal Organ and Marrow Function (supportive care is allowed per institutional
             standards, i.e. filgrastim, transfusion)

               -  Absolute neutrophil count (ANC) ≥ 750/uL*

               -  Platelet count ≥ 50,000/uL*

               -  Absolute lymphocyte count ≥ 150/uL*

             Adequate renal, hepatic, pulmonary and cardiac function defined as:

               -  Creatinine within institutional norms for age (i.e. ≤ 2 mg/dL in adults or
                  according to table below in children <18 years) OR creatinine clearance (as
                  estimated by Cockcroft Gault Equation) ≥ 60 mL/min Age (Years) Maximum Serum
                  Creatinine (mg/dL)

                    -  5 Years - Serum Creatinine (mg/dL) = 0.8; 5 < age ≤ 10 Years - Serum
                       Creatinine (mg/dL) = 1.0; >10-18 years - Serum Creatinine (mg/dL) = 1.2; >
                       18 years - Serum Creatinine (mg/dL) = 2.0

               -  Serum (alanine aminotransferase/aspartate aminotransferase(ALT/AST)≤ 10x upper
                  limit of normal (ULN) (unless elevated ALT/AST is associated with leukemia
                  involvement of the liver, in which case this criterion will be waived and not
                  disqualify a patient).

               -  Total bilirubin ≤ 1.5 mg/dl, except in subjects with Gilbert's syndrome.

               -  Cardiac ejection fraction ≥ 45%, no evidence of physiologically significant
                  pericardial effusion as determined by an ECHO,

               -  No clinically significant ECG findings

               -  No clinically significant pleural effusion

               -  Baseline oxygen saturation > 92% on room air * if these cytopenias are not judged
                  by the investigator to be due to underlying disease (i.e. potentially reversible
                  with anti-neoplastic therapy); A subject will not be excluded because of
                  pancytopenia ≥ Grade 3 if it is due to disease, based on the results of bone
                  marrow studies.

         11. CNS Status Subjects with CNS involvement are eligible as long as there are no overt
             signs or symptoms that in the evaluation of the investigator would mask or interfere
             with the neurological assessment of toxicity.

         12. Pregnancy Test Females of childbearing potential must have a negative serum or urine
             pregnancy test (females who have undergone surgical sterilization or who have been
             postmenopausal for at least 2 years are not considered to be of childbearing
             potential)

         13. Contraception Subjects of child bearing or child fathering potential must be willing
             to practice birth control from the time of enrollment on this study and for four (4)
             months after receiving the preparative regimen or for as long as CD19/CD22-CAR T cells
             are detectable in peripheral blood.

         14. Ability to give informed consent. All subjects ≥ 18 years of age must be able to give
             informed consent. For subjects <18 years old their legal authorized representative
             (LAR) (i.e. parent or guardian) must give informed consent. Pediatric subjects will be
             included in age appropriate discussion and verbal assent will be obtained for those >
             7 years of age, when appropriate. If a minor becomes of age during participation of
             this study, he/she will be asked to reconsent as an adult

        EXCLUSION CRITERIA:

          1. Recurrent or refractory ALL limited to isolated testicular disease.

          2. Hyperleukocytosis (≥ 50,000 blasts/μL) or rapidly progressive disease that in the
             estimation of the investigator and sponsor would compromise ability to complete study
             therapy

          3. History of malignancy other than non-melanoma skin cancer or carcinoma in situ (e.g.
             cervix, bladder, breast) unless disease free for at least 3 years

          4. Presence of fungal, bacterial, viral, or other infection that is uncontrolled or
             requiring IV antimicrobials for management. Simple urinary tract infection (UTI) and
             uncomplicated bacterial pharyngitis are permitted if responding to active treatment.

          5. Ongoing infection with HIV or hepatitis B (HBsAg positive) or hepatitis C virus (anti
             HCV positive) as the immunosuppression contained in this study will pose unacceptable
             risk. A history of hepatitis B or hepatitis C is permitted if the viral load is
             undetectable per quantitative polymerase chain reaction (PCR) and/or nucleic acid
             testing.

          6. CNS disorder such as cerebrovascular ischemia/hemorrhage, dementia, cerebellar
             disease, or any autoimmune disease with CNS involvement hat in the judgment of the
             investigator may impair the ability to evaluate neurotoxicity.

          7. History of myocardial infarction, cardiac angioplasty or stenting, unstable angina, or
             other clinically significant cardiac disease within 12 months of enrollment.

          8. Any medical condition that in the judgement of the sponsor investigator is likely to
             interfere with assessment of safety or efficacy of study treatment

          9. History of severe immediate hypersensitivity reaction to any of the agents used in
             this study.

         10. Women of child bearing potential who are pregnant or breastfeeding because of the
             potentially dangerous effects of the preparative chemotherapy on the fetus or infant.

         11. In the investigators judgment, the subject is unlikely to complete all protocol
             required study visits or procedures, including follow up visits, or comply with the
             study requirements for participation

         12. Has primary immunodeficiency or history of autoimmune disease (e.g. Crohns, rheumatoid
             arthritis, systemic lupus) requiring systemic immunosuppression/systemic disease
             modifying agents within the last 2 years.