It sounds like a virus to me and I will attempt to point you in the right direction. I have never had this virus but a lot of people have. It goes without saying that you should have an anti-virus program running and up to date.
Now some links to get you started:

WARNING: Viruses on network you should be aware of!

LimeWire continually Popping up every few seconds & also Opening at System Startup

LimeWire popping up - how to eradicate it

Good luck.

Here's one more: Limewire Acting Wierd (PLEASE HELP!!!)

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