 This single center Phase I dose escalation trial will evaluate the safety, tolerability and efficacy of LBH589 when combined with capecitabine and lapatinib in three parts. Part 1 will determine the maximum tolerated doses MTD of LBH589 when combined with capecitabine. Parts 2 and 3 will be limited to locally recurrent or metastatic breast cancer patients, ICH 3 overexpression or FISH amplification documented locally. Part 2 will evaluate the safety of the MTD of LBH589 determined in Part 1 when paired with lapatinib 1000 mg by mouth PO daily. Parts 2 and 3 will be limited to locally recurrent or metastatic breast cancer patients, ICH 3 overexpression or FISH amplification documented locally. Part 3 will evaluate the tolerability and effectiveness of the triplet combination, LBH589, capecitabine and lapatinib in breast cancer patients. 