OUTLINE: Patients receive docetaxel IV over 60 minutes and carboplatin IV over 30 minutes on day 1, trastuzumab (Herceptin®) IV over 30-90 minutes on days 1, 8, and 15, and oral lapatinib ditosylate on days 1-21 (TCHL). Treatment with TCHL repeats every 3 weeks for 6 courses in the absence of disease progression or unacceptable toxicity. Patients then receive trastuzumab IV over 30-90 minutes on day 1 and oral lapatinib ditosylate on days 1-21 (days 1-7 of course 12 only) (LT). Treatment with LT repeats every 3 weeks for 12 courses in the absence of disease progression or unacceptable toxicity..