Doxorubicin and Cyclophosphamide Followed By Trastuzumab, Paclitaxel, and Lapatinib in Treating Patients With Early-Stage HER2-Positive Breast Cancer That Has Been Removed By Surgery

DISEASE CHARACTERISTICS: * Histologically confirmed diagnosis of early-stage breast cancer * HER2 positive by immunohistochemistry (IHC) (3+) or fluorescent in situ hybridization (FISH) * Ductal carcinoma in situ (DCIS) components should not be counted in the determination of degree of IHC staining or FISH amplification * No locally advanced tumors (i.e., T4) at diagnosis, including the following: * Tumors fixed to chest wall * Peau d'orange * Skin ulcerations or nodules * Clinical inflammatory changes (e.g., diffuse brawny cutaneous induration with an erysipeloid edge) * Has undergone mastectomy or lumpectomy with axillary node or sentinel node dissection within the past 84 days * Patients who have undergone a mastectomy must meet the following criteria: * No evidence of gross or microscopic tumor (i.e., invasive DCIS) at the surgical resection margins noted in final surgery or pathology reports * Patients with close margins are eligible * Radiation therapy is required for 4 or more positive lymph nodes and must be started after completion of chemotherapy * Patients who have undergone a lumpectomy with axillary node or sentinel node dissection must meet the following criteria: * No evidence of invasive cancer or DCIS at the surgical resection margins * No gross residual adenopathy * Planning to undergo radiation therapy to the breast with or without regional lymphatics after completion of chemotherapy * No active hepatic or biliary disease * Patients with liver metastases, stable chronic liver disease, Gilbert's syndrome, or asymptomatic gallstones are eligible * Hormone receptor status: * Estrogen receptor and progesterone receptor status known PATIENT CHARACTERISTICS: * Male or female * Menopausal status not specified * ECOG performance status 0-2 * Absolute neutrophil count ≥ 1,500/mm³ * Platelet count ≥ 100,000/mm³ * Hemoglobin ≥ 10.0 g/dL * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * AST and ALT ≤ 2.5 times ULN * Alkaline phosphatase ≤ 2.5 times ULN * Creatinine normal OR creatinine clearance ≥ 60 mL/min * LVEF ≥ 50% by MUGA scan or echocardiogram * Able to complete questionnaire(s) by themselves or with assistance * Able and willing to provide blood and tissue samples * No known sensitivity to benzyl alcohol * No sensory neuropathy ≥ grade 2 * No active cardiac disease, including any of the following: * Myocardial infarction within the past 6 months * Prior or concurrent congestive heart failure * Prior or concurrent arrhythmia or cardiac valvular disease requiring medications or that is clinically significant * Uncontrolled hypertension, defined as diastolic blood pressure (BP) \>100 mm Hg or systolic BP \> 200 mm Hg on 2 separate occasions ≥ 14 days apart * Clinically significant pericardial effusion * Prior or concurrent uncontrolled or symptomatic angina * Other cardiac condition that, in the opinion of the treating physician, would put the patient at hazardous risk * No history of allergic reactions attributed to compounds of similar chemical or biologic composition as lapatinib ditosylate * No uncontrolled intercurrent illness including, but not limited to, the following: * Ongoing or active infection * Psychiatric illness or social situations that would preclude study compliance * Able to swallow and retain oral medication * No history of gastrointestinal (GI) disease resulting in an inability to take oral medication, including any of the following: * Malabsorption syndrome * Requirement for IV alimentation * Prior surgical procedures affecting absorption * Uncontrolled inflammatory GI disease (e.g., Crohn's disease or ulcerative colitis) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 6 months after completion of study treatment PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No prior chemotherapy, radiation therapy, immunotherapy, or biotherapy for breast cancer * No primary breast radiation therapy as part of breast-conserving treatment * No prior anthracycline or taxane therapy for any malignancy * No prior epidermal growth factor receptor-targeting therapies (e.g., gefitinib, cetuximab, erlotinib hydrochloride, rituximab, trastuzumab \[Herceptin®\], lapatinib ditosylate, panitumumab, or nimotuzumab) * At least 14 days since prior and no concurrent CYP3A4 inducers, including the following: * Rifamycin-class antibiotics (e.g., rifampin, rifabutin, or rifapentine) * Anticonvulsants (e.g., phenytoin, carbamazepine, or barbiturates \[e.g., phenobarbital\]) * Antiretrovirals (e.g., efavirenz or nevirapine) * Glucocorticoids (e.g., oral cortisone, hydrocortisone, prednisone, methylprednisolone, or dexamethasone) * Daily oral dexamethasone ≤ 1.5 mg (or equivalent) allowed * Modafinil * Hypericum perforatum (St. John's wort) * At least 7 days since prior and no concurrent CYP3A4 inhibitors, including the following: * Antibiotics (e.g., clarithromycin, erythromycin, or troleandomycin) * Antifungals (e.g., itraconazole, ketoconazole, fluconazole \[\> 150 mg daily\], or voriconazole) * Antiretrovirals and protease inhibitors (e.g., delaviridine, nelfinavir, amprenavir, ritonavir, indinavir, saquinavir, or lopinavir) * Calcium channel blockers (e.g., verapamil or diltiazem) * Antidepressants (e.g., nefazodone or fluvoxamine) * Gastrointestinal agents (e.g., cimetidine or aprepitant) * Grapefruit and grapefruit juice * At least 6 months since prior and no concurrent amiodarone * No herbal or alternative medicines or supplements ≥ 14 days before, during, and for 30 days after completion of study treatment * No concurrent hormonal agents (e.g., birth control pills, ovarian hormonal replacement therapy, or raloxifene) * Adjuvant hormonal agents (e.g., tamoxifen, aromatase inhibitors) allowed after completion of chemotherapy as part of treatment for breast cancer * No concurrent antiretroviral therapy for HIV-positive patients * No concurrent digitalis or beta-blockers for congestive heart failure * No concurrent arrhythmia or angina pectoris medication * No other concurrent investigational agents or anticancer therapies, including cytotoxic agents or immunotherapy