This is normal Gnutella network traffic. Whenever you are connected to the network, large volumes of search queries are being sent to your computer, which makes it appear that you have been downloading large files. When a search query matches a file in your library, a search result is generated and sent across the network to other computer users who are searching for files. This would account for the large masses of data leaving your computer.

You shouldn't have to worry about unauthorized file downloading with LimeWire. But if you are on a static IP internet connection, I would recommend using a heavy-duty firewall just in case you do get any intruders.
:-)