You can delete files from LW's library after they've been added to the iTunes library as long as the file is still saved somewhere on your computer. If you don't want the files in LW's library any more, you can save them into a different folder somewhere.
Remember that the 'your name's LimeWire tunes' in iTunes is just a playlist & doesn't contain actual music files.
How to transfer music to my iPod (& iTunes)

Or, in iTunes go Edit > Preferences > Advanced. Tick the box to copy files to iTunes Music folder when adding to library > ok. Now songs will be saved to your iTunes Music folder when you add them to the iTunes library & you can delete those files from LW's library.
Adding Content to iTunes
When you delete from LW's library - use the option to send files to the recycle bin... that way, you can restore the files if you run into problems!!

If you just delete files from LW's library & don't make sure that they're saved somewhere on your computer - iTunes won't be able to find the files & then you'll see the ! symbol beside the file in iTunes, when you try to play it