Sorafenib in Treating Non-Smokers or Former Light Smokers With Relapsed or Refractory Stage IIIB or Stage IV Non-Small Cell Lung Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed non-small cell lung cancer * Stage IIIB or IV disease * Recurrent disease after prior surgery, chemotherapy, or radiotherapy * No squamous cell histology or mixed tumor with \> 50% squamous cells * Non-smoker (smoked ≤ 100 cigarettes in lifetime) OR former light smoker (smoked \> 100 cigarettes but ≤ 10 pack years AND quit smoking ≥ 1 year ago) * No known brain metastasis * Patients with neurological symptoms must undergo a CT scan or MRI of the brain to exclude brain metastasis PATIENT CHARACTERISTICS: * ECOG(Eastern Cooperative Oncology Group)performance status 0-2 * ANC (Absolute Neutrophil Count)≥ 1,500/mm³ * Platelet count ≥ 100,000/mm³ * ALT (Alanine Aminotransferase Test) and AST (Aspartate Aminotransferase Test) ≤ 2.5 times upper limit of normal (ULN) * Alkaline phosphatase ≤ 2.5 times ULN * Bilirubin ≤ 1.5 mg/dL * Creatinine clearance ≥ 50 mL/min * INR (International Normalized Ratio) \< 1.5 OR PT/PTT (Prothrombin time/partial thromboplastin time)normal * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective barrier contraception prior to, during, and for ≥ 3 months after completion of study treatment * No cardiac disease, including any of the following: * New York Heart Association class III-IV congestive heart failure * Unstable angina (anginal symptoms at rest) * New-onset angina within the past 3 months * Myocardial infarction within the past 6 months * No cardiac ventricular arrhythmias requiring anti-arrhythmic therapy * No uncontrolled hypertension (i.e., systolic blood pressure \[BP\] \> 150 mm Hg or diastolic BP \> 90 mm Hg) despite optimal medical management * No thrombolic or embolic events (e.g., cerebrovascular accident, including transient ischemic attacks) within the past 6 months * No pulmonary hemorrhage or bleeding event ≥ CTCAE (Common Terminology Criteria for Adverse Events)grade 2 within the past 4 weeks * No other hemorrhage or bleeding event ≥ CTCAE grade 3 within the past 4 weeks * No active clinically serious infection \> CTCAE grade 2 * No serious non-healing wound, ulcer, or bone fracture * No evidence or history of bleeding diathesis or coagulopathy * No known HIV infection or chronic hepatitis B or C * No other malignancy except for any of the following: * Adequately treated basal cell or squamous cell skin cancer * In situ cervical cancer * Other cancer from which the patient has been disease-free for ≥ 5 years with a low probability of recurrence * No condition that impairs the patient's ability to swallow whole pills * No malabsorption problems * No known or suspected allergy to sorafenib tosylate or any agent given in the course of this study * No significant traumatic injury within the past 4 weeks PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No more than one prior systemic chemotherapy treatment for metastatic disease * Prior treatment with EGFR inhibitors is not considered chemotherapy * More than 4 weeks since prior major surgery or open biopsy * No prior sorafenib tosylate * No concurrent St. John's wort or rifampin * Concurrent anticoagulation with warfarin or heparin allowed