My goal is to get Limewire(JAVA) and Songbird(XULRunner) to run together.
I was thinking the best way is to run the XUL application(songbird) inside
The official XUL implementation by Mozilla and is heavily dependent on Gecko. Gecko is not written in Java nor embedded in AWT/Swing/SWT (at least without using JNI).
So, the short answer is: no. You must either use JNI or use heavy, complex and incomplete third party libaries.
However, JavaXPCOM seems to allow embedding Gecko: https://developer.mozilla.org/en/JavaXPCOM But in that case you'll depend on Gecko... and I don't know if that's enough to run Songbird.