LW is no longer supported on OSX 10.3, thus you will need to install an earlier version
Lime Wire » Download Out-Of-Date Installers
If problems installing: You get the "null" message in the Apple installer when a OS X thinks a more recent version is installed. Double-click the harddrive icon, open the Library, open the Receipts folder, then find the file: Install LimeWire.pkg, delete it and try again.