Brief Summary: RATIONALE: Lapatinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as vinorelbine, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving lapatinib together with vinorelbine may kill more tumor cells. PURPOSE: This phase I trial is studying the side effects and best dose of lapatinib when given together with vinorelbine in treating patients with advanced solid tumors.

Detailed Description: OBJECTIVES: Primary * Determine the safety and feasibility of 2 different schedules of lapatinib ditosylate when administered with vinorelbine ditartrate in patients with advanced solid tumors. Secondary * Determine the maximum tolerated dose (MTD) of each of these regimens in these patients. * Determine, preliminarily, the efficacy of these regimens in these patients. * Examine tissue and blood specimens from these patients to investigate potential predictors of response. * Determine the pharmacokinetics of lapatinib ditosylate and vinorelbine ditartrate in patients treated at the MTD. OUTLINE: This is a phase I study comprising 2 separate, sequential dose-escalation studies of lapatinib ditosylate. Patients are assigned to 1 of 2 treatment groups. * Group A (daily dosing): Patients receive oral lapatinib ditosylate once daily on days 1-28 and vinorelbine ditartrate IV on days 1, 8, and 15. Cohorts of 3-6 patients receive escalating doses of lapatinib ditosylate until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 2 of 3 or 2 of 6 patients experience dose-limiting toxicity during course 1. At least 6 patients are treated at the MTD. Once the MTD of lapatinib has been determined, patients may be accrued to group B or to a separate pharmacokinetics cohort in group A. * Pharmacokinetics (PK) cohort\*: Patients in the PK cohort receive vinorelbine ditartrate IV as in group A and oral lapatinib ditosylate once daily at the MTD on days 3-28 (course 1 only) and on days 1-28 in all subsequent courses. Patients undergo PK sampling during course 1. NOTE: \*Accrual to group B and to the PK cohort of group A may occur simultaneously. * Group B (intermittent dosing): Patients receive oral lapatinib ditosylate once daily at the MTD on days 2-5, 9-12, and 16-25 and vinorelbine ditartrate IV, on days 1, 8, and 15. In both groups and in the PK cohort, treatment repeats every 28 days for 6 courses in the absence of disease progression or unacceptable toxicity. Patients who have completed 6 courses of combined therapy may receive additional courses with lapatinib ditosylate alone. Patients undergo blood collection and buccal brushings periodically for pharmacokinetic and biomarker correlative studies. Archival tumor tissue is also evaluated for biomarkers, including epidermal growth factor receptor (EGFR) and HER-2/neu expression levels, EGFR polymorphisms and gene mutations (including RAS), levels of cellular proliferation and apoptosis, and RAS mutations by immunohistochemistry, mutation analysis, TUNEL assay, and polymerase chain reaction. After completion of study treatment, patients are followed for 30 days. PROJECTED ACCRUAL: A total of 66 patients will be accrued for this study.