I actually gave you 3 techniques. (1.) Of course the drag & drop.
(2.) Consolidate iTunes to see if the limwire that appears within iTunes playlist will copy its files to iTunes library folders.
(3). Create a playlist(s) within LW & export that as an m3u file. Import that file as a playlist & then consolidate iTunes. This way (& technique (1)) definitely works but I'm curious to know if technique (2) will also work. I'll try it myself in several hours to see if it does. Else you can try it & get back to us.