You may have this problem because, although you have installed the Java 2 Runtime Environment version 1.3.1 or greater, the launcher/shell script is still referring to an older version present on your system.

I was able to solve this problem by editing runLime.sh in my LimeWire directory and explicitly calling the java executable in the directory of the newer version.

that is, in runLime.sh, I changed:
java -jar RunLime.jar

to
/home/imp/jre1.3.1_03/bin/java -jar RunLime.jar

You'll want to replace /home/imp/jre1.3.1_03 with wherever you have installed the newer java version. Note that the /bin subdirectory is where the java executable is located.

then run LimeWire using:
sh runLime.sh

from the LimeWire directory.

This worked for me, anyway.
Good luck.

-imp