Paclitaxel and Trastuzumab With or Without Lapatinib in Treating Patients With Stage II or Stage III Breast Cancer That Can Be Removed by Surgery

This randomized phase III trial studies paclitaxel and trastuzumab with or without lapatinib to see how well they work in treating patients with stage II or stage III breast cancer that can be removed by surgery. Drugs used in chemotherapy, such as paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Monoclonal antibodies, such as trastuzumab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Lapatinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving paclitaxel with trastuzumab and/or lapatinib before surgery may make the tumor smaller and reduce the amount of normal tissue that needs to be removed. It is not yet known which regimen is more effective in treating patients with breast cancer.

Inclusion Criteria: * Pathologic confirmation of invasive breast cancer; patients with inflammatory breast cancer are not eligible * Clinical stage II-III operable invasive breast cancer with intent to perform surgical resection after neoadjuvant therapy * Patients with multicentric or bilateral disease are eligible as long as the target lesion meets the eligibility criteria for this study * Staging to rule out metastatic disease is recommended for clinical stage III patients * Tumors must be HER2 positive defined as HER2 3+ by immunohistochemical (IHC) assays or gene amplification by fluorescence in situ hybridization (FISH) with a ratio of \>= 2 on invasive tumor * Estrogen receptor (ER) and progesterone receptor (PgR) status must be known * The target lesion in the breast must be \>= 1 cm on physical examination or by radiographic measurement; palpable axillary adenopathy will be documented but not serve as measurable disease for the primary endpoint; patients with axillary disease only are not eligible to participate * Patient agrees to provide pretreatment biopsies * No prior chemotherapy, hormone therapy, biologic, or radiation therapy with therapeutic intent for this cancer * Cardiac ejection fraction must be \>= 50% by echocardiogram or multiple gated acquisition (MUGA) scan * Eastern Cooperative Oncology Group (ECOG) (Zubrod) performance status 0-1 * Patients must not be pregnant or nursing * Absolute neutrophil count (ANC) \>= 1,000/ul * Platelet count \>= 100,000/ul * Bilirubin =\< 1.5 times upper limit of normal * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 times upper limit of normal (ULN) * Serum beta-human chorionic gonadotropin (HCG) negative (in female patients unless status-post (s/p) hysterectomy or menopausal or no menses for 24 consecutive months); assay must have a sensitivity of at least 50 mIU/mL