Fulvestrant With or Without Lapatinib in Treating Postmenopausal Women With Stage III or Stage IV Breast Cancer That is Hormone Receptor-Positive

PRIMARY OBJECTIVES: I. To compare the effect, in terms of progression free survival, of the antiestrogen fulvestrant alone with fulvestrant administered in combination with the dual-kinase inhibitor lapatinib for postmenopausal women with estrogen receptor (ER) and/or progesterone receptor (PgR) positive advanced breast cancer. SECONDARY OBJECTIVES: I. To compare the effects of fulvestrant alone with fulvestrant and lapatinib on other clinical endpoints, including response rate, response and stable disease rate (complete response \[CR\] + partial response \[PR\] + stable disease \>= 6 months), duration of response, overall survival, symptom checklist scores, and toxicity. II. To define predictive markers of clinical activity among women receiving fulvestrant with or without lapatinib. III. To determine if the clinical benefits for combination of hormonal and growth factor inhibitor therapy are most pronounced in women whose tumors express higher levels of ER, epidermal growth factor receptor (EGFR), human epidermal growth factor receptor 2 (HER2), phosphorylated protein kinase B (pAkt), and/or phosphorylated mitogen-activated protein kinase 1/2 (pERK1/2). IV. To serologically determine if HER2 extracellular domain (ECD) and EGFR ECD levels can identify patients with a greater likelihood of response and clinical benefit to fulvestrant with or without lapatinib. OUTLINE: Patients are randomized to 1 of 2 treatment arms. ARM I: Patients receive lapatinib ditosylate orally (PO) once daily (QD) on days 1-28 and fulvestrant intramuscularly (IM) on days 1 and 15 of course 1 and on day 1 of each subsequent course. ARM II: Patients receive placebo PO QD on days 1-28 and fulvestrant as in Arm I. In both arms, treatment repeats every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 6 months for 2 years and then annually for 3 years.