Patients receive doxorubicin hydrochloride IV and cyclophosphamide IV on day 1. Treatment repeats every 2-3 weeks for 4 courses. Patients then receive paclitaxel IV over 60 minutes and trastuzumab (Herceptin®) IV over 90 minutes on days 1, 8, and 15 and oral lapatinib ditosylate on days 1-21. Treatment with paclitaxel, trastuzumab, and lapatinib repeats every 3 weeks for up to 4 courses. Patients then receive trastuzumab IV over 30-90 minutes on day 1 and oral lapatinib ditosylate on days 1-21. Treatment with trastuzumab and lapatinib ditosylate repeats every 3 weeks for up to 12 courses.