On the Limewire main window go to Tools>Options

Up top of the Vertical list of catagories, you should see "Saving" go to that.

It will say the defualt location your files are saved in.

Also, for each file type, you can specify a different location for each one if you like (ex. music into My Music, pics in My Pictures etc etc)

Take note of where your "Video" files are saved to and the .avi you are looking for should be in there.