This randomized phase III trial studies fulvestrant and lapatinib to see how well they work compared to fulvestrant and a placebo in treating postmenopausal women with stage III or stage IV breast cancer that is hormone receptor-positive. Estrogen can cause the growth of breast cancer cells. Hormone therapy using fulvestrant may fight breast cancer by lowering the amount of estrogen the body makes. Lapatinib may stop the growth of breast cancer cells by blocking some of the enzymes needed for cell growth. It is not yet known whether fulvestrant is more effective with or without lapatinib in treating breast cancer.