I had some java errors as well when trying:

sh ./LimeWireLinux.bin

I installed jre1.3.1_02 (downloaded from http://java.sun.com/j2se/1.3/jre/)
as instructed on the limewire.com download page. I then ran the command:
/usr/java/jre1.3.1_02/bin/java LimeWireLinux.bin (one line) and got a nice little GUI taking me through the install process. It said that the install was successful, however, when I looked at the install log, it said nothing was installed.
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