Erlotinib With or Without Fulvestrant in Treating Patients With Stage IIIB or Stage IV Non-Small Cell Lung Cancer

RATIONALE: Erlotinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Estrogen can cause the growth of non-small cell lung cancer cells. Hormone therapy using fulvestrant may fight non-small cell lung cancer by lowering the amount of estrogen the body makes. Giving erlotinib together with fulvestrant may kill more tumor cells. It is not yet known whether giving erlotinib together with fulvestrant is more effective than erlotinib alone in treating non-small cell lung cancer. PURPOSE: This randomized phase II trial is studying giving erlotinib together with fulvestrant to see how well it works compared to erlotinib alone in treating patients with stage IIIB or stage IV non-small cell lung cancer.