Which version of LW are you trying to install? LimeWire 4.12.15 is the last version OSX 10.3.9 can install. You will find it on the versions link on the LW download page.
If you installed LW 5, you will need to trash the
install limewire.pkg file from the Receipts folder;
Receipts folder sample image. Then you will be able to install LW 4.12.