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)