Gefitinib and Sirolimus in Treating Patients With Recurrent 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 or refractory disease * Received ≥ 1 prior platinum-containing chemotherapy regimen * Unidimensionally measurable disease that has not been irradiated * No newly diagnosed untreated brain metastases or spinal cord compression * Paraffin-embedded tumor tissue or slides available PATIENT CHARACTERISTICS: Age * 18 and over Performance status * ECOG 0-2 Life expectancy * Not specified Hematopoietic * Adequate bone marrow function * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 Hepatic * Adequate hepatic function * No severe or uncontrolled hepatic disease Renal * Adequate renal function * Creatinine ≤ 3.0 times upper limit of normal * No severe or uncontrolled renal disease Cardiovascular * Adequate cardiac function * No severe or uncontrolled cardiac disease * No uncontrolled hyperlipidemia Pulmonary * No unstable or uncompensated respiratory disease * No clinically active interstitial lung disease * Patients with chronic stable radiographic changes who are asymptomatic are eligible Gastrointestinal * Able to take oral medication * No gastrointestinal condition (e.g., peptic ulcer disease) that would affect absorption Other * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No serious infection * No known severe hypersensitivity to gefitinib or any of its excipients * No other malignancy within the past 5 years except treated basal cell or squamous cell skin cancer or carcinoma in situ of the cervix * No other severe or uncontrolled systemic disease * No significant clinical disorder or laboratory finding that would preclude study participation PRIOR CONCURRENT THERAPY: Biologic therapy * More than 14 days since prior biologic therapy * No prior cetuximab, panitumumab, or bevacizumab Chemotherapy * See Disease Characteristics * More than 4 weeks since prior cytotoxic chemotherapy Endocrine therapy * Not specified Radiotherapy * See Disease Characteristics * More than 3 weeks since prior radiotherapy * No concurrent radiotherapy Surgery * Recovered from prior oncologic or other major surgery * No prior gastrointestinal surgery affecting absorption * No concurrent surgery, including ophthalmic surgery, during and for 1 week after study treatment Other * Recovered from all prior therapy * More than 30 days since prior investigational agents * No other prior HER1/epidermal growth factor receptor axis agents, including the following: * Gefitinib * Erlotinib * CI-1033 * Lapatinib * No other prior vascular endothelial growth factor axis agents, including the following: * ZD6474 * Vatalanib * No concurrent CYP3A4 inducers, including the following: * Phenytoin * Carbamazepine * Rifampin * Phenobarbital * Barbiturates * Hypericum perforatum (St. John's wort) * No other concurrent systemic treatment for the malignancy * No concurrent bisphosphonates for symptomatic bone metastases * No concurrent systemic retinoids