This is an open-label, Phase I study of oral topotecan administered in combination with lapatinib in subjects with advanced solid tumors. This Phase I study will evaluate the safety, tolerability, and pharmacokinetics of oral topotecan administered in combination with lapatinib. This study will be conducted in two parts. Part 1 of the study will investigate the impact of lapatinib on the bioavailability of oral topotecan (bioavailability phase) and Part 2 of the study will consist of dose finding to determine the maximum-tolerated dose (MTD) regimen of the combination (dose escalation phase). In Part 2 of the study, the dose of oral topotecan will be escalated while lapatinib will be given initially as fixed doses. The primary objective of the study is to determine the MTD regimen of oral topotecan administered for five-consecutive days every 21 days in combination with daily lapatinib in subjects with advanced solid tumors.