Modified Immune Cells (AFM13-NK) and A Monoclonal Antibody (AFM13) in Treating Patients With Recurrent or Refractory CD30 Positive Hodgkin or Non-Hodgkin Lymphomas

Inclusion Criteria: * Patients with a diagnosis of relapsed or refractory classical Hodgkin lymphoma (HL), anaplastic large cell lymphoma (ALCL), peripheral T-cell lymphoma not otherwise specified (PTCL-NOS), mycosis fungoides (MF), or B-cell non-Hodgkin lymphoma with a pre-enrollment tumor biopsy positive for CD30 by immunohistochemistry at \>= 1%. Patients with HL, ALCL and MF must be refractory or intolerant to brentuximab vedotin. * Karnofsky performance status \>= 60%. * Absolute neutrophil count \>= 500/mm\^3 * Platelet count \>= 50,000/mm\^3 * Serum creatinine clearance \>= 50 ml/min, estimated using the Cockcroft-Gault equation. * Alanine aminotransferase (ALT) and/or aspartate aminotransferase (AST) =\< 3 x upper limit of normal (ULN). * Bilirubin =\< 2 x ULN. * Alkaline phosphatase (ALP) =\< 2 x ULN. * Forced expiratory volume in 1 second (FEV1) \>= 50% * Forced vital capacity (FVC) \>= 50% * Carbon monoxide diffusing capability test (DLCO) (corrected for hemoglobin \[Hgb\]) \>= 50% * Left ventricular ejection fraction \>= 40%. * No uncontrolled arrhythmias or symptomatic cardiac disease. * If female of child-bearing potential, must not be pregnant or be breastfeeding and required to have a negative urine or serum pregnancy test within 3 days prior to the first dose of study drug. * Note: Urine pregnancy tests that cannot be confirmed as negative, require a confirmatory negative serum pregnancy test. In addition, females of childbearing potential must agree use …