GCC 0845:Vorinostat and Lapatinib in Advanced Solid Tumors and Advanced Breast Cancer to Evaluate Response and Biomarkers

Inclusion Criteria: * Age greater than or equal to 18 years. * Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to 2. * Consent for peripheral blood sampling for analysis of circulating tumor cells. * Patients must have adequate organ and marrow function as defined by the protocol. * Female patients with histologically confirmed adenocarcinoma of the breast with recurrent local-regional disease, or metastatic disease that have progressed after treatment with regimens that include an anthracycline, a taxane, or trastuzumab. * Human Epidermal growth factor Receptor 2 (HER2) positive in the primary or secondary tumor tissue as defined by: * Grade 3plus staining intensity (on a scale of 0 to 3) by means of Immunohistochemistry (IHC) analysis OR * Gene amplification on fluorescence in situ hybridization (FISH) greater than or equal to 2.2. * Patients must have measurable disease by the Response Evaluation Criteria In Solid Tumors (RECIST)criteria at the time of enrollment. * Prior trastuzumab therapy is allowed. Trastuzumab should be stopped at least 4 weeks prior to enrollment. Exclusion Criteria: * Patients receiving any other investigational agents. * Prior exposure to lapatinib, vorinostat, or other Histone deacetylase (HDAC) inhibitors. Prior valproic acid exposure is allowed providing this is a greater than or equal to 30 days wash-out period. * History of allergic reactions or hypersensitivity to compounds of similar chemical or biologic composition to vorinostat or lapatinib. * Patients with history of clinically significant or uncontrolled cardiac disease, as defined by the protocol, or any significant cardiac condition that in the judgment of the investigator is unsuitable. * Significant chronic or recent (less than 30 days) acute gastrointestinal disorder with diarrhea as a major symptom (e.g. Crohn's disease, malabsorption, or Grade 2 or greater diarrhea of any etiology at baseline). * Prior exposure to more than 360 mg/m2 doxorubicin or liposomal doxorubicin, more than 120 mg/m2 mitoxantrone, or more than 90 mg/m2 idarubicin, or elevated baseline cardiac troponin T (more than upper limit of normal). * Patients with active Central Nervous System (CNS) metastasis and/or carcinomatous meningitis are excluded. Patients with CNS metastasis who have completed a course of therapy would be eligible for the study provided they are clinically stable for 3 weeks prior to entry as defined as: (1) no evidence of new or enlarging CNS metastasis and (2) off steroids and/or anticonvulsants, for at least 4 weeks before an enrollment. * Female patient that is pregnant or breastfeeding or expecting to conceive during the study. Women able to have children must have a negative pregnancy test prior to enrollment. All patients must use two effective methods of contraception (including a barrier method) during treatment and for 12 weeks after stopping treatment. * The patient is known to be Human immunodeficiency virus (HIV), Hepatitis B, or Hepatitis C-positive (test results are not required in order to participate). * Patients with current active hepatic or biliary disease (with exception of patients with Gilbert's syndrome, asymptomatic gallstones, liver metastases or stable chronic liver disease per investigator assessment) * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirement. * Previous or current systemic malignancy within the past 3 years other than the following: Female- breast cancer or adequately treated carcinoma in-situ of the cervix, or Female and Male- basal/squamous carcinoma of the skin.