It appears that there are versions of Java available for QNX,
which is all you need to get LimeWire to run.

Check out:

http://www.embedded.oti.com/learn/vaesvm.html

It appears that you can download their JVM for free as well. Once you have it installed, your should download the version of LimeWire for Linux or Solaris, and follow the same steps outlined in those readmes to get it to run.

It would be great if you could let us know of any successes or failures you experience setting this up.