A Study of Lapatinib in Combination With Everolimus in Patients With Advanced, Triple Negative Breast Cancer

Inclusion Criteria: * Histologically or cytologically confirmed ER(-), PR(-), HER2(-) locally advanced or metastatic breast cancer * Disease progression following prior first line cytotoxic chemotherapy in metastatic setting * At least 1 lesion measurable by Response Evaluation Criteria in Solid Tumors (RECIST) criteria * Age \>18 years old * Female * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Left ventricular ejection fraction (LVEF) \> 50% * Absolute neutrophil count (ANC)\>1500/mm3; platelets \>100,000/mm3; hemoglobin \> 9 g/dL; serum creatinine \< 1.5x upper limit of normal (ULN); total bilirubin \< 1.5x ULN, aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 2.5x ULN * Patients must be recovered from both acute and late effects of any prior surgery, radiotherapy or other antineoplastic therapy * Patients or their legal representatives must be able to read, understand and provide informed consent to participate in the trial. * Patients of childbearing potential agree to use an effective form of contraception during the study and for 90 days following the last dose of study medication (an effective form of contraception is an oral contraceptive or a double barrier method) Exclusion Criteria: * Patients with current active hepatic or biliary disease (except for patients with Gilbert's syndrome, asymptomatic gallstones, liver metastases or stable chronic liver disease per investigator assessment) * Patients with an active infection or with a fever \> 101.3 Fahrenheit within 3 days of the first scheduled day of protocol treatment * Patients with active central nervous system (CNS) metastases. Patients with stable CNS disease, who have undergone radiotherapy at least 4 weeks prior to the planned first protocol treatment and who have been on a stable dose of corticosteroids for 3 weeks are eligible for the trial * History of prior malignancy within the past 5 years except for curatively treated basal cell carcinoma of the skin or cervical intra-epithelial neoplasia with two consecutive normal pap smears 6 months apart * Patients who received radiotherapy to more than 25% of their bone marrow; or patients who received radiotherapy to target lesions within 4 weeks of entry * Patients who are receiving concurrent investigational therapy * Peripheral neuropathy \>= Grade 2 * Patients who are pregnant or lactating * Any other medical condition, including mental illness or substance abuse, deemed by the Investigator to be likely to interfere with a patient's ability to sign informed consent, cooperate and participate in the study, or interfere with the interpretation of the results. * History of allogeneic transplant * Known HIV or Hepatitis B or C (active, previously treated or both)