-  INCLUSION CRITERIA:

        Malignancy Criteria:

          -  Patients must have anaplastic large cell lymphoma, angioimmunoblastic T-cell lymphoma,
             peripheral T-cell lymphoma not otherwise specified, diffuse large B-cell lymphoma not
             otherwise specified, primary mediastinal B-cell lymphoma, grey zone lymphoma,
             enteropathy-associated T-cell lymphoma, or extranodal NK/T-cell lymphoma, nasal type

          -  Clear CD30 expression must be detected on 75% or more of malignant cells from either
             bone marrow or lymphoma mass by flow cytometry or immunohistochemistry. The patient s
             malignancy will need to be assessed for CD30 expression by flow cytometry or
             immunohistochemistry performed at the NIH. If unstained, paraffin-embedded bone marrow
             or lymphoma sections are available from prior biopsies, these can be used to determine
             CD30 expression by immunohistochemistry; otherwise, patients will need to come to the
             NIH for a biopsy to determine CD30 expression. The sample for CD30 expression can come
             from a biopsy obtained at any time before enrollment, unless the patient has received
             a prior anti-CD30 monoclonal antibody, in which case the sample must come from a
             biopsy following completion of the most recent anti-CD30 monoclonal antibody
             treatment.

          -  Eligible patients with diffuse large B-cell lymphoma or primary mediastinal B-cell
             lymphoma must have received 2 prior treatment regimens at least 1 of which included an
             anthracycline and an anti-CD20 monoclonal antibody.

          -  Patients must have measurable malignancy as defined by at least one of the criteria
             below.

          -  Lymphoma mass that is measurable (minimum 1.5 cm in largest diameter) by CT scan is
             required unless bone marrow lymphoma is detectable.

          -  For a lymphoma mass to count as measurable malignancy, it must have abnormally
             increased metabolic activity when assessed by positron emission tomography (PET) scan.

          -  For lymphoma with only bone marrow involvement, no mass is necessary, but if a mass is
             not present, bone marrow malignancy must be detectable by flow cytometry.

        Other Inclusion Criteria:

          -  Greater than or equal to 18 years of age and less than or equal to age 73.

          -  Able to understand and sign the Informed Consent Document.

          -  Clinical performance status of ECOG 0-2

          -  Room air oxygen saturation of 92% or greater

          -  Male patients and must be willing to practice birth control from the time of
             enrollment on this study and for four months following the final CAR T-cell infusion.
             Pre-menopausal patients (female patients who have had a menstrual period within the
             last year) must be willing to practice birth control from the time of enrollment and
             for one year following the final CAR T cell infusion.

          -  Seronegative for HIV antibody. (The experimental treatment being evaluated in this
             protocol depends on an intact immune system. Patients who are HIV seropositive can
             have decreased immune -competence and thus are less responsive to the experimental
             treatment and more susceptible to its toxicities.)

          -  Seronegative for HTLV-1.

          -  Negative for hepatitis B surface antigen. Positive hepatitis B tests can be further
             evaluated by confirmatory tests; and if confirmatory tests are negative, the patient
             can be enrolled.

          -  Seronegative for hepatitis C antibody unless antigen negative. If hepatitis C antibody
             test is positive, then patients must be tested for the presence of RNA by RT-PCR and
             be HCV RNA negative to be enrolled.

          -  A patient with a prior history of hepatits B or a prior history of hepatitis C may
             participate, as long as the patient s viral hepatitis has been treated, and the
             patient has no detectable HBV DNA or HCV RNA.

          -  At time of protocol enrollment, the patient should be negative for CMV by antibody
             testing or by PCR. In case of disagreement between these 2 CMV tests, the tests will
             be repeated and Dept. of Laboratory Medicine consulted.

          -  Absolute neutrophil count greater than or equal to 1000/mm3 without the support of
             filgrastim or other growth factors.

          -  Platelet count greater than or equal to 55,000/mm3

          -  Hemoglobin greater than 8.0 g/dl. Transfusion support is allowed.

          -  Less than 5% malignant cells in the peripheral blood leukocytes

          -  Serum ALT and AST less or equal to 3 times the upper limit of the institutional normal
             unless liver involvement by malignancy is demonstrated.

          -  Serum creatinine less than or equal to 1.6 mg/dL.

          -  Total bilirubin less than or equal to 2.0 mg/dl.

          -  At least 14 days must have elapsed since any prior systemic therapy prior to apheresis
             and prior to the initiation of chemotherapy (including systemic corticosteroids at
             doses greater than prednisone 5 mg/day or the equivalent corticosteroid doses).
             Because this protocol requires collection of autologous blood cells by leukapheresis
             in order to prepare CAR T cells, systemic anti-malignancy therapy including systemic
             corticosteroid therapy at doses greater than prednisone 5 mg/day or the equivalent
             corticosteroid doses is not allowed within 14 days prior to the required
             leukapheresis. NOTE: Because of the long half-life and potential to affect CAR
             T-cells, 30 days must elapse from the time of administration of anti-PD-1 or
             anti-PD-L1 antibodies or other agents that in the opinion of the PI can stimulate
             immune activity and infusion of CAR T-cells.

          -  Normal cardiac ejection fraction (greater than or equal to 50% by echocardiography)
             and no evidence of hemodynamically significant pericardial effusion as determined by
             an echocardiogram within 4 weeks of the start of the treatment protocol.

          -  Patients must not take corticosteroids at doses higher than 5 mg/day of prednisone or
             the equivalent for 14 days before apheresis, and for 14 days prior to the conditioning
             chemotherapy regimen.

          -  Patients must be willing to undergo endotracheal intubation, mechanical ventilation,
             dialysis, CPR, and electrical defibrillation. Patients must be willing to receive
             vasopressor drugs and all other standard intensive care unit interventions. Any living
             will must be amended to allow these interventions or the patient will not eligible.

          -  Patients who have been treated on other protocols of genetically-modified T-cells at
             the NIH only are potentially eligible under these conditions:

               -  At least 6 months have elapsed since the last genetically-modified T-cell therapy
                  that the patient received and there is no evidence of replication-competent
                  retroviruses (evidence must be provided from prior NIH gene-therapy protocol
                  Principal Investigator) and persisting genetically-modified T cells are not
                  detectable in the patient s blood (evidence must be provided by prior NIH
                  gene-therapy protocol Principal Investigator).

        Additional Inclusion Criteria Pertinent Only for Patients with Prior Allogeneic
        Transplantation:

          -  Recipients must have received an 9/10 or 10/10 HLA-matched sibling allogeneic
             hematopoietic stem cell transplant, or a 9/10 or 10/10 HLA-matched unrelated donor
             (URD) allo-HSCT for an eligible CD30+ lymphoma.

          -  Donor T cell engraftment after allo-HSCT (>90% donor chimerism of the T-cell
             compartment).

          -  Patients must be at least 90 days post-transplant.

          -  Patients must be off all systemic immunosuppressive drugs including corticosteroids at
             doses of greater than 5 mg/day prednisone or equivalent, if given for treatment of
             graft versus host disease, for at least 28 days prior to protocol enrollment and must
             remain off immunosuppressive drugs while enrolled on the protocol. Patients must not
             be taking any systemic steroids at doses greater than 5 mg/day prednisone or
             equivalent at all for 14 days prior to apheresis and initiation of chemotherapy.
             Topical corticosteroid preparations applied to the skin such as solutions, creams, and
             ointments are allowed. Inhaled corticosteroids are allowed, and corticosteroid eye
             drops are allowed.

          -  Prior DLIs are not necessary.

          -  Either no evidence of GVHD or minimal clinical evidence of acute GVHD and chronic GVHD
             while off of systemic immunosuppressive therapy for at least 28 days. Minimal clinical
             evidence of acute GVHD defined as grade 0 to I acute GVHD 109 Minimal evidence of
             chronic GVHD is defined as mild global score chronic GVHD (as defined by the 2005 NIH
             consensus project) or no chronic GVHD .107 Subjects with disease that is controlled to
             stage I acute GVHD or to mild global score chronic GVHD with local topical cutaneous
             steroids will be eligible for enrollment.

        EXCLUSION CRITERIA:

          -  Patients with Hodgkin lymphoma are no longer eligible for participation (as of
             amendment G, Protocol version: 08/12/2019).

          -  Patients that require urgent therapy due to tumor mass effects or spinal cord
             compression.

          -  Patients with lymphoma masses 10.0 cm or larger in longest diameter will not be
             eligible.

          -  Patients that have active hemolytic anemia.

          -  Patients who are currently taking any medications for systemic anticoagulation other
             than aspirin will not be eligible.

          -  Patients with second malignancies in addition to their lymphoma are not eligible if
             the second malignancy has required treatment (including maintenance therapy) within
             the past 4 years or is not in complete remission. There are two exceptions to this
             criterion:

        successfully treated non-metastatic basal cell or squamous cell skin carcinoma.

          -  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.
             Women of child-bearing potential are defined as all women except women who are
             postmenopausal or who have had a hysterectomy. Postmenopausal will be defined as women
             over the age of 55 who have not had a menstrual period in at least 1 year.

          -  Active uncontrolled systemic infections (defined as infections causing fevers and
             infections requiring intravenous antibiotics when the intravenous antibiotics have
             been administered for less than 72 hours); active coagulation disorders or other major
             uncontrolled medical illnesses of the cardiovascular, respiratory, endocrine, renal,
             gastrointestinal, genitourinary or immune system; history of myocardial infarction;
             history of idiopathic ventricular tachycardia or ventricular fibrillation in the past
             12 months or history of ventricular tachycardia or ventricular fibrillation (VT/VF)
             associated with VT/VF risk factors (e.g., QT prolongation and cardiomyopathy); active
             cardiac arrhythmias (Active atrial fibrillation is not allowed, but resolved atrial
             fibrillation is allowed.); active obstructive or restrictive pulmonary disease; or
             active autoimmune diseases such as rheumatoid arthritis.

          -  Patients will not be seen for screening appointments or enrolled on the protocol if
             they have been hospitalized within the 7 days prior to the screening appointment or
             the date of protocol enrollment.

          -  Any form of primary immunodeficiency (such as Severe Combined Immunodeficiency
             Disease) , unless the immunodeficiency has been cured by allogeneic stem cell
             transplant.

          -  Systemic corticosteroid therapy at doses greater than 5 mg/day of prednisone or the
             equivalent dose is not allowed within 14 days prior to the required leukapheresis, or
             the initiation of the conditioning chemotherapy regimen. Corticosteroid creams,
             ointments, and eye drops are allowed.

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

          -  Patients with current CNS involvement by malignancy (either by imaging or
             cerebrospinal fluid involvement or biopsy-proven).

          -  Patients currently taking anticoagulants.