Did you reinstall Java first, using the offline installer? Point 1 below.
Fixes for LimeWire

Did you also use the offline installer for LW?

Also try deleting LW's preferences when LW's completely closed (check in task manager to see if it's running). That's points 2 & 3 above.
You could change compatibility too, that's point 5.

If none of this helps, make sure that LW's on the list of exceptions/allowed apps for any antispyware you're using. Have you updated or changed any security programs/settings recently?

Oops, got beaten. You can try these other things if deleting the preferences doesn't work!