I am in-vin-ci-ble!
I am invincible!
I believe that I just now became the first person in the entire world to run LimeWire under Java SE6 on Mac OS X. You see, SE6 is 64-bit only, and Carbon is 32-bit only. The two do not play well together.
So, after commenting out some non-essential, Carbon-dependent functionality, and replacing the other Carbon-dependent things with JNI implementations, it actually ran.
Downloading doesn't seem to be working, but, ah, whatever. Good enough for a victory dance.