I'm having the same problem. I downloaded the latest JRE from java.sun.com but I get a ton of failed dependencies if I try to install it. Plus, the path to libawt.so in the error message below does not exist on my machine.

Starting LimeWire...
Java exec found in PATH. Verifying...
Suitable java version found [java = 1.4.2]
Configuring environment...
Loading LimeWire:
reflect - bad awtHandle.
/usr/lib/jvm/java-1.4.2-ibm-1.4.2.1/jre/jre/lib/i386/libawt.so: cannot open shared object file: No such file or directory

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Something went wrong with LimeWire.
Maybe you're using the wrong version of Java?
(LimeWire is tested against and works best with with Sun's JRE, Java 1.4+)
The version of Java in your PATH is:
java version "1.4.2"
Java(TM) 2 Runtime Environment, Standard Edition (build 1.4.2)
Classic VM (build 1.4.2, J2RE 1.4.2 IBM build cxia32142-20041210 (JIT enabled: jitc))