Can you go to the LimeWire Menu and get "About LimeWire"?

It should list the version of LW and of Java.

It would also help to post the version of OS X that your iMac is using. You can get that from the Apple Menu>About this Mac

All that aside, if you can shut your computer down for 2 minutes, and restart holding the shift key, this will help clear the virtual memory that has been a problem for some users for quite a while (we keep hoping Apple will put out a java update).