I have had these problems too with SuSE 7.1 Professional. Here is what I did to fix the problem.

In Xwindows, I opened a terminal, and typed:

xhost +

I then su'd to root:

su -

I then set my display:

export DISPLAY=:0

I then ran the installer:

sh ./LimeWireLinux.bin

And the GUI appeared and I was running.