This phase II trial studies how well capecitabine, cyclophosphamide, lapatinib ditosylate, and trastuzumab work in treating patients with human epidermal growth factor receptor 2 (HER2)-positive metastatic breast cancer. Drugs used in chemotherapy, such as capecitabine and cyclophosphamide, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving capecitabine and cyclophosphamide daily may kill more tumor cells. Lapatinib ditosylate may stop the growth of tumor cells by blocking some of the enzymes needed for growth. Monoclonal antibodies, such as trastuzumab, can block tumor growth in different ways. Some block the ability of the tumor to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Giving capecitabine, cyclophosphamide, lapatinib ditosylate, and trastuzumab together may be an effective treatment for breast cancer.