Hello,
Try this:
Turn off your computer (completely shut it down).
Then, disconnect your ethernet cable (or whatever cable type you are using for your Internet connection).
Then, leave that cable / connection disconnected.
Now, turn on your computer.
Then, try to remove the file and folder that are related to LimeWire.
See if that works.
Check out this article for a little understanding as to why I propose this method to attempt removal:
http://www.123macmini.com/forums/viewtopic.php?t=6720&sid=8d05d72d780ae73188e946 7009dfd24f
Now, once you have made sure that everything is removed from your system, then go ahead and empty your trash and turn off the computer.
Reconnect your cables, and turn it back on.
Note that you can reconnect the cables with the computer on, but I would restart the computer anyway. So, either turn off and reconnect the cables, or restart and reconnect the computers.
I hope this helps.
Let us know if you have other questions.
P.S., if you'd like, go ahead and click the "Helpful" or "Solved" buttons on any of the posts / replies above if you feel they were helpful or adequately answered your question.