Lapatinib With Carboplatin and Paclitaxel in Esophagus and Gastroesophageal Junction (GEJ)

Inclusion Criteria: * Patients must have a histologic diagnosis of adenocarcinoma of the esophagus, or gastroesophageal junction based on biopsy material or adequate cytologic exam. * Patients must have incurable metastatic or recurrent adenocarcinoma of esophagus or gastroesophageal junction. * Patients must have an ECOG performance status of 0-1. * Patients must have adequate bone marrow function as evidence by: absolute neutrophil count \> 1500/uL, and platelet count \> 100,000/uL * Patients must have adequate renal function as evidenced by a Cockcroft-Gault calculated creatinine clearance \> 30 mL/min. * Patient must have adequate hepatic function as evidenced by: serum total bilirubin \< 2.0 mg/dl, and AST/ALT \< 3 X the institutional upper limit of normal. Patients with an elevated unconjugated bilirubin (Gilbert's syndrome) will be eligible if hepatic enzymes and function are otherwise completely normal (AST/ALT/Alk Phos within normal limits), and there is no evidence of hemolysis. * Patients must have cardiac ejection fraction \> 50% as measured by echocardiogram or MUGA scan. * Patient must agree to stop medications or substances known to affect, or with the potential to affect the activity or pharmacokinetics of lapatinib. (See Appendix I). * Patients must be able to adhere to the study visit schedule and other protocol requirements. * Patients must have measurable/evaluable disease as per RECIST 1.1 criteria. * Tumor must be tested for HER2 and EGFR before patient registration. * Patients of childbearing potential must 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). * Patients must be \>18 years old. * Women of childbearing potential must have a negative pregnancy test prior to enrollment. * Patients must have a life expectancy \>12 weeks. * Patients must be able to tolerate oral (or feeding-tube administered) medications. Exclusion Criteria: * Patients with any other diagnosis except for adenocarcinoma (squamous cell carcinoma, small cell carcinoma, lymphoma, etc) will be ineligible. * Patients with another active malignancy within the last 5 years will not be eligible except for curatively treated basal cell carcinoma of the skin, cervical intra-epithelial neoplasia, or localized prostate cancer with PSA \<1.0 mg/dL on 2 successive evaluations at least 3 months apart, with the most recent evaluation within 4 weeks of entry. * Patients may not have had any previous chemotherapy for recurrent or metastatic disease and no chemotherapy or radiation therapy within the past 4 weeks. * Patients may not have received any previous treatment with carboplatin, paclitaxel, or a HER2 or EGFR inhibitor prior to enrollment. * Patients may not be receiving any other investigational agents or other concurrent anticancer therapy. * Patients with brain metastases are excluded. * Patients with \> grade 2 peripheral neuropathy per NCI's Common Toxicity Criteria Version 4.0 will be ineligible. * Males with QTc \> 450 or females with QTc \> 470msec will be ineligible. * Patients with active cardiac disease are excluded including current uncontrolled or symptomatic angina, history of clinically significant arrhythmias requiring medications, (with the exception of asymptomatic atrial tachycardias requiring anticoagulation and/or beta-blockade), myocardial infarction \< 6 months from study entry, uncontrolled or symptomatic congestive heart failure, or any other cardiac condition, which in the opinion of the treating physician, would make this protocol unreasonably hazardous for the patient * Women who are currently pregnant or lactating will be ineligible. * Any other uncontrolled inter-current medical or psychiatric illness. * Known HIV-positive patients will be excluded. * Patients with any gastrointestinal disease resulting in an inability to take oral )or feeding-tube administered medication, malabsorption syndrome, a requirement for IV alimentation, prior surgical procedures affecting absorption, or uncontrolled inflammatory GI disease (e.g., Crohn's, ulcerative colitis). * Concomitant requirement for medication classified as CYP3A4 inducers or inhibitors.