Lapatinib Ditosylate in Treating Patients With a Rising PSA Indicating Recurrent Prostate Cancer

Inclusion Criteria:

* Histologically confirmed diagnosis of prostate cancer
* Previous treatment with definitive surgery or radiation therapy
* Prior salvage therapy (surgery, radiation, or other local ablative procedures) is allowed if the intent was for cure
* No evidence of metastatic disease on physical exam, computed tomography (CT) (magnetic resonance imaging \[MRI\]), and bone scan
* Prior neoadjuvant/adjuvant hormonal or chemotherapy and investigational agents are allowed if it was last used \>= 1 year prior to enrollment (no prior vaccine/immunotherapy for prostate cancer will be allowed)
* No therapy modulating testosterone levels (such as luteinizing-hormone releasing-hormone agonists/antagonists and antiandrogens) is permitted within 1 year prior to enrollment; agents such as 5alpha-reductase inhibitors, ketoconazole, megestrol acetate, systemic steroids, or herbal supplements are not permitted at any time during the period that the PSA values are being collected
* Hormone-sensitive prostate cancer as evident by a serum total testosterone level \> 150 ng/dL within 4 weeks prior to registration
* All patients must have evidence of biochemical progression as determined by a reference PSA value followed by 2 rising PSA values, each higher than the previous value, obtained at least 6 weeks apart; all of these PSA values must be obtained at the same reference lab, and all must be done within 6 months prior to enrollment
* The most recent of the PSA values must be greater than 0.4 ng/ml (after prostatectomy) or greater than 1.5 ng/ml (after radiation therapy) at time of enrollment; this measurement must be obtained within 6 months prior to enrollment
* PSA doubling time (PSADT) must be =\< 365 days
* Eastern Cooperative Oncology Group (ECOG) Performance Status 0-1
* Leukocytes \>= 3000/mm\^3
* Granulocytes \>= 1500/mm\^3
* Platelet count \>= 100,000/mm\^3
* Serum creatinine within normal institutional limits or creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Serum total bilirubin within normal institutional limits
* Serum alkaline phosphatase within normal institutional limits
* Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamic pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2.5 x institutional upper limit of normal
* Cardiac ejection fraction within the institutional range of normal, as measured by echocardiogram or multi gated acquisition scan (MUGA) scan within 4 weeks prior to registration; note that baseline and on-treatment scans should be performed using the same modality and preferably at the same institution
* No unstable arrhythmias on electrocardiogram (ECG) are allowed (rate controlled, asymptomatic atrial fibrillation is allowed)
* No concomitant use of any medication classified as cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4) inducer or inhibitor; for patients previously treated with one of these prohibited medications, the prohibited agent needs to be discontinued, either 7 days, 14 days, or 6 months prior to the administration of the first dose of study medication
* Human immunodeficiency virus (HIV)-positive patients receiving combination anti-retroviral therapy are excluded from the study; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated
* Normal prothrombin time (PT)/international normalized ratio (INR) within 4 weeks prior to registration
* Able to swallow and retain oral medication
* Patients with gastrointestinal (GI) tract disease resulting in an inability to take oral medication, malabsorption syndrome, a requirement for intravenous (IV) alimentation, prior surgical procedures affecting absorption, uncontrolled inflammatory GI disease (e.g., Crohn's, ulcerative colitis) will not be eligible
* Sexually active males are strongly advised to use an accepted and effective method of contraception
* Patients may not be receiving any other investigational agents or receiving concurrent anticancer therapy
* No history of allergic reactions attributed to compounds of similar chemical or biologic composition to GW572016
* No uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* No other malignancies permitted within the past 5 years with the exception of non-melanoma skin cancer treated with curative intent