Cyclophosphamide or Denileukin Diftitox Followed By Expanding a Patient's Own T Cells in the Laboratory in Treating Patients With HER-2/Neu Overexpressing Metastatic Breast Cancer, Ovarian Cancer, or Non-Small Cell Lung Cancer Previously Treated With HER-2/Neu Vaccine

Inclusion Criteria: * Patients with progressive HER2/neu overexpressing metastatic breast, ovarian, or non-small cell lung cancer not considered curable by conventional therapies, including trastuzumab * Extra-skeletal disease that can be accurately measured \>= 10 mm by standard imaging techniques that can include but not limited to computed tomography (CT), positron emission tomography (PET), magnetic resonance imaging (MRI) * Skeletal or bone-only disease which is measurable by Fludeoxyglucose F 18 (FDG) PET imaging will also be allowed * Patients with ovarian cancer may have measurable disease; however, their only indication of progression may be an abnormal CA-125 * Patients must have documented HER-2/neu overexpression in their tumor (either primary or metastasis) as was required per the eligibility criteria of their original vaccination protocol * Patients must have received HER2-specific vaccinations while enrolled on a HER2 vaccine protocol approved at the University of Washington Human Subjects Division * Patients must have undergone leukapheresis after vaccination through a protocol approved at the University of Washington Human Subjects Division and have product stored for clinical use * Subjects must have a Performance Status Score (Zubrod/Eastern Cooperative Oncology Group \[ECOG\] Scale) = 0 or 1 * Patients can be currently receiving trastuzumab and/or lapatinib and/or hormonal therapy and/or bisphosphonate therapy * Patients on trastuzumab and/or lapatinib must have adequate cardiac function as demonstrated by multi gated acquisition (MUGA) scan or echocardiogram (ECHO) within 90 days of eligibility determination * Patients must be off all immunosuppressive treatments, and/or systemic steroid therapy, for at least 14 days prior to initiation of study treatment * Patients must be off chemotherapy and trastuzumab for at least 1 week prior to the first infusion of T cells * Men and women of reproductive ability must agree to contraceptive use during the study and for one month after the final T cell infusion * Patients with a history of brain metastases must have a stable head imaging study within 30 days of enrollment * White blood cells (WBC) \>= 3000/mm\^3 * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Hemoglobin (Hgb) \>= 10 mg/dl * Platelets \>= 75,000mm\^3 * Serum creatinine =\< 2.0 mg/dl or creatinine clearance \> 60 ml/min * Total bilirubin =\< 2.5 mg/dl * Aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) =\< 3 times ULN Exclusion Criteria: * Concurrent enrollment in other treatment studies * Patients with any of the following cardiac conditions: * Symptomatic restrictive cardiomyopathy * Unstable angina within the last 4 months prior to enrollment * New York Heart Association functional class III-IV heart failure on active treatment * Patients with any clinically significant autoimmune disease uncontrolled with treatment * Pregnant or breast-feeding women * Known history of hypersensitivity to diphtheria toxin or interleukin (IL)-2 (only for subjects enrolled in Group B)