Normaly You have the JDK 1.1.8 or higher on the actuall Linux-Distributions. On my system vers. 1.1.8 JDK is running without any problems with LimeWire 1.4.

You can check it out with java -version or jre

Download the LimeWireOther.zip to your system, go to the Download-Directory where the Zip-file is and type "java -classpath LImeWireOther.zip install" and it should work (if your JDK or JRE is newer than 1.1.7. No idea, if it is working with 1.1.7).

Good luck.