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

RATIONALE: Gefitinib and everolimus may stop the growth of tumor cells by blocking the enzymes necessary for their growth. Giving gefitinib together with everolimus may kill more tumor cells. PURPOSE: This phase I/II trial is studying the side effects, best way to give, and best dose of giving gefitinib with everolimus and to see how well it works in treating patients with stage IIIB or stage IV or recurrent non-small cell lung cancer.