I was able to work around the problem by getting the tarball (LimeWireLinux.tgz) from LimeWire.com (thanks guys for putting that out there, else I'd be pooched!). I unpacked the tarball, changed into the new directory I put the files into, and executed:
export PATH=/usr/java/j2re1.4.1_01/bin:$PATH && sh ./runLime.sh

But I still can't explain why I couldn't install with the .bin file.

I tried
export LAX_DEBUG && ./LimeWire-2.8.4.bin
but didn't find anything useful.

My install of RedHat 7.3 was completely basic (e.g. I selected NO packages during install) and I have been adding on packages and dependancies for KDE, XMMS, NVidia drivers, a few games, a compiled GAIM, Mozilla+Galeon, and that's about it. There's little else to conflict here.

If anyone has any ideas why I couldn't use the regular installer, please post them so others might benefit.

Thanks,
/dev/idal