There is a reported incompatibility with java on occasions (search for posts by "jum"), but I'm not sure if yours is the same one. Did you also find a JavaNativeCrash_pid*.log as well as the LimeWire.crash.log?

Usually a safe boot/repair permissions works to get me running on a G3 iBook (especially after going through a number of Software Updates), but only rarely do I find reinstalling java worth a try.

sounds silly, but try trashing the dock icon and making a new one (Would be nice if this would be the fix!)