Dasatinib in Treating Patients With Stage IIIB, Stage IV, or Recurrent Non-Small Cell Lung Cancer

Inclusion Criteria: * Platelet count \>= 100,000/mm\^3 * Histologically or cytologically confirmed non-small cell lung cancer meeting 1 of the following criteria: * Stage IV disease * Stage IIIB disease with pleural effusion * Recurrent disease after surgery or radiotherapy * Measurable disease, defined as \>= 1 lesion that can be accurately measured in at least 1 dimension (longest diameter to be recorded) \>= 20 mm by conventional techniques OR \>= 10 mm by spiral CT scan * Previously treated brain metastasis allowed, provided there is no bleeding, no midline shift, no need for steroids or anti-convulsants, and no symptoms * Must agree to obtain residual tumor tissue available from the existing diagnostic biopsy tumor tissue * Eastern cooperative oncology group (ECOG) performance status (PS) 0-1 OR Karnofsky PS 60-100% * Life expectancy \> 12 weeks * White blood cell (WBC) \>= 3,000/mm\^3 * Absolute neutrophil count \>= 1,500/mm\^3 * Bilirubin =\< 1.5 times upper limit of normal (ULN) * Aspartate aminotransferase (AST) and ALT =\< 2.5 times ULN * Creatinine =\< 3 times ULN OR Creatinine clearance \>= 60 mL/min * No uncontrolled congestive heart failure or potentially life-threatening arrhythmia * No angina at rest * No neuropathy \>= grade 2 * No chronic diarrhea or history of inflammatory bowel disease * No history of pulmonary fibrosis (other than in an irradiated field) * No other concurrent serious medical illness * O2 saturation \> 92% on room air * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No history of allergic reactions to compounds of similar chemical or biological composition to dasatinib * No heart rate-corrected QT interval (QTc) prolongation (i.e., QTC \>= 480 msec) or other significant ECG abnormalities that could lead to adverse effects if the QTc interval were prolonged * No medical condition that impairs the ability to swallow, retain, or absorb dasatinib including, but not limited to, any of the following: * Gastrointestinal tract disease resulting in an inability to take oral medication, requirement for IV alimentation, prior surgical procedures affecting absorption, active peptic ulcer disease * No myocardial infarction or ventricular tachyarrhythmia within the past 6 months * left ventricular ejection fraction (LVEF) normal * No major conduction abnormality (unless cardiac pacemaker is present) * No ongoing or active infection * No history of significant bleeding disorder (congenital \[von Willebrand's disease\] or acquired \[antifactor VIII antibodies\]) * No psychiatric illness or social situation that would preclude study compliance * No prior chemotherapy or biologic therapy for recurrent or metastatic non-small cell lung cancer * Adjuvant cytotoxic chemotherapy after surgical resection or chemotherapy with radiation for locally advanced disease (curative intent) allowed provided disease recurrence \>= 3 months after completion of last chemotherapy dose * Measurable disease must be outside the radiotherapy port OR clearly growing inside the port * No prior radiotherapy to \>= 25% of the marrow-containing skeleton * At least 7 days since prior and no concurrent medications that are inhibitors or inducers of CYP3A4 * At least 7 days since prior and no concurrent agents with proarrhythmic potential * No other concurrent investigational agents * No other concurrent anticancer agents or therapies * No concurrent antiretroviral therapy for HIV-positive patients * No concurrent systemic antacids (H2 receptor antagonists and proton pump inhibitors) * Locally acting antacids allowed except for 2 hours before and after dasatinib administration