T Cells Expressing a Fully-Human Anti-CD30 Chimeric Antigen Receptor for Treating CD30-Expressing Lymphomas

* 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 natural killer (NK)/T-cell lymphoma, nasal type * Clear TNFRSF8 (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 National Institutes of Health (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-B-lymphocyte antigen CD20 (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 computed tomography (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 Eastern Cooperative Oncology Group (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 Human T-cell lymphotropic virus type 1 (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 ribonucleic acid (RNA) by Reverse transcription polymerase chain reaction (RT-PCR) and be Hepatitis C (HCV) RNA negative to be enrolled. * A patient with a prior history of hepatitis 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 Hepatitis B (HBV) deoxyribonucleic acid (DNA) or HCV RNA. * At time of protocol enrollment, the patient should be negative for cytomegalovirus (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/mm\^3 without the support of filgrastim or other growth factors. * Platelet count greater than or equal to 55,000/mm\^3 * Hemoglobin greater than 8.0 g/dl. Transfusion support is allowed. * Less than 5% malignant cells in the peripheral blood leukocytes * Serum alanine aminotransferase (ALT) and aspartate aminotransferase (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-Programmed cell death protein 1 (PD-1) or anti-Programmed death-ligand 1 (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, cardiopulmonary resuscitation (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 National Institutes of Health (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-Hematopoietic stem-cell transplantation (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 donor lymphocyte infusions (DLIs) are not necessary. * Either no evidence of graft versus host (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 central nervous system (CNS) involvement by malignancy (either by imaging or cerebrospinal fluid involvement or biopsy-proven). * Patients currently taking anticoagulants.