Inclusion Criteria:

          -  RECIPIENT: Patients with high risk or relapsed disease who are planning to receive, or
             have received prior allogeneic HSCT from an human leukocyte antigen (HLA)-matched
             related, or HLA-mismatched related donor; high risk is defined as patients with acute
             lymphoblastic leukemia who have delayed clearance of minimal residual disease,
             Philadelphia (Ph)-like, or complex, 11q23 or hypodiploid karyotype

          -  RECIPIENT: Available donor who provided hematopoietic stem-cell (HSC)

          -  RECIPIENT: Patients with CD19+ lymphoid malignancies that are refractory to or
             intolerant of standard treatment (as defined below):

               -  B-cell Acute Lymphoblastic Leukemia (ALL)

               -  Non-Hodgkin lymphoma (NHL) to include diffuse large B-cell lymphoma (DLBCL) not
                  otherwise specified, primary mediastinal large B cell lymphoma, mantle cell
                  lymphoma, or transformed follicular lymphoma (TFL) as defined by the World Health
                  Organization 2008 criteria

               -  Small lymphocytic lymphoma (SLL)

               -  Chronic lymphocytic leukemia (CLL)

               -  NOTE: Refractory disease for acute and chronic leukemia is defined by:

                    -  Presence of > 5% malignant blasts in bone marrow and/or peripheral blood
                       and/or minimal residual disease by flow cytometry or molecular analysis for
                       fusion proteins and/or positive imaging for extra-medullary disease to most
                       recent therapy

               -  NOTE: Refractory disease for lymphoma is defined as:

                    -  Progressive disease or stable disease lasting =< 6 months, as best response
                       to most recent chemotherapy regimen; or disease progression or recurrence =<
                       12 months after prior ASCT

                    -  Prior therapy must have included an anti-CD20 monoclonal antibody-containing
                       regimen and an anthracycline-containing chemotherapy regimen

                    -  For patients with TFL, prior chemotherapy for follicular lymphoma and
                       subsequent refractory disease after transformation to DLBCL

                    -  At least one measurable lesion according to revised International Working
                       Group (IWG) Response Criteria

          -  RECIPIENT: In patients with prior transplant, treatment will begin no earlier than 3
             months post-transplant. Enrollment can occur earlier to allow time for donor cell
             collection

          -  RECIPIENT: Karnofsky performance scale > 60

          -  RECIPIENT: Patient able to provide written informed consent

          -  RECIPIENT: Patient able to provide written informed consent for the long-term
             follow-up (LTFU) gene therapy study

          -  RECIPIENT: Negative human anti-mouse antibody (HAMA)

          -  DONOR: HLA-matched related, HLA-mismatched related, including haploidentical donor, or
             related donor cleared to donate based on Stem Cell Transplantation and Cellular
             Therapy (SCTCT) standard-of-care (SOC) guidelines

          -  DONOR: Negative beta HCG in female of child-bearing potential defined as:

               -  Not post-menopausal for 12 months, or

               -  No previous surgical sterilization, or

               -  Lactating females

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: Patient must have measurable disease at
             the time of treatment

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: Not received anti-thymocyte globulin
             (ATG), Campath, or other T-cell immunosuppressive antibodies or donor-lymphocyte
             infusion in the 28 days prior to T-cell infusion

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: Serum creatinine < 2 x upper limit of
             normal (ULN)

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: Alanine aminotransferase (ALT)/aspartate
             aminotransferase (AST) =< 2.5 x ULN or =< 5 x ULN if documented liver metastases

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: Total bilirubin =< 1.5 mg/dL, except in
             patients with Gilbert's syndrome in whom total bilirubin must be =< 3.0 mg/dL

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: Cardiac ejection fraction >= 40%, and no
             clinically-significant electrocardiogram (ECG) findings

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: No clinically significant pleural
             effusion, baseline oxygen saturation > 90% on room air

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: No evidence of grade >= 2 active graft
             versus host disease (GVHD) using the Center for International Blood and Marrow
             Transplant Research (CIBMTR) Acute GVHD Grading System or requiring systemic steroid
             therapy greater than physiologic dosing at time of starting treatment

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: Non-hematologic toxicity grade >= 2
             (Common Terminology Criteria for Adverse Events [CTCAE] version 5) related to the
             lymphodepleting chemotherapy until the toxicity has resolved to grade =< 1 and the
             patient is afebrile

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: No new grade > 2 neurologic, pulmonary,
             cardiac, gastrointestinal, renal or hepatic (excluding albumin) toxicity

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: Serum creatinine < 2 x ULN

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: Oxygen saturation > 90% on room air

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: Active clinically significant infection
             within 7-days of study treatment

          -  T-CELL INFUSION REQUIREMENTS FOR RECIPIENT: Using an investigational agent

        Exclusion Criteria:

          -  RECIPIENT: Positive beta human chorionic gonadotropin (HCG) in female of child-bearing
             potential defined as not post-menopausal for 12 months or no previous surgical
             sterilization or lactating females

          -  RECIPIENT: Patients with allergy to mouse products or cetuximab

          -  RECIPIENT: Active central nervous system (CNS) disease in patient with history of CNS
             malignancy

          -  RECIPIENT: Positive serology for human immunodeficiency virus (HIV)

          -  RECIPIENT: Active hepatitis B or active hepatitis C

          -  RECIPIENT: Has received a T-cell product within 6 weeks prior to planned infusion of
             genetically modified T cells