Gefitinib and Everolimus in Treating Patients With Stage IIIB or Stage IV or Recurrent Non-Small Cell Lung Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed non-small cell lung cancer (NSCLC) meeting 1 of the following stage criteria: * Stage IIIB (unresectable, with malignant pleural or pericardial effusion) * Stage IV disease * Recurrent disease * Measurable or evaluable indicator lesions * Progressive disease after receiving ≥ 1 prior chemotherapy regimen that included cisplatin or carboplatin and docetaxel * No uncontrolled brain or leptomeningeal metastases * Must not require concurrent glucocorticoids for control of metastases PATIENT CHARACTERISTICS: Age * 18 and over Performance status * Karnofsky 70-100% OR * ECOG 0-2 Life expectancy * Not specified Hematopoietic * WBC ≥ 3,000/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Hemoglobin ≥ 9.0 g/dL Hepatic * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * AST ≤ 2.5 times ULN Renal * Creatinine ≤ 1.5 times ULN OR * Creatinine clearance ≥ 60 mL/min Cardiovascular * No congestive heart failure * No New York Heart Association class III or IV heart disease * No unstable angina Other * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No severe infection * No severe malnutrition * No other serious medical illness * No other malignancy within the past 3 years except adequately treated basal cell or squamous cell skin cancer or carcinoma of the cervix PRIOR CONCURRENT THERAPY: Biologic therapy * No concurrent biologic therapy * No concurrent immunotherapy Chemotherapy * See Disease Characteristics * No prior conventional chemotherapy for metastatic or recurrent NSCLC (phase II only) * At least 4 weeks since prior chemotherapy * No other concurrent chemotherapy Endocrine therapy * See Disease Characteristics * No concurrent oral steroids for management of skin toxicity Radiotherapy * At least 4 weeks since prior radiotherapy * No concurrent radiotherapy Surgery * At least 4 weeks since prior major surgery * No concurrent surgery for an identifiable lesion Other * Recovered from all prior therapy * No prior gefitinib, erlotinib, or other epidermal growth factor tyrosine kinase inhibitor * No concurrent cytotoxic therapy (e.g., methotrexate for rheumatoid arthritis) * No other concurrent oncolytic agents