1. The LW playlist which shows up on iTunes is simply a playlist. The songs don't belong to iTunes Music Library.
2. iTunes is able to use DAAP which enables playlists to be shared across a network. But these playlists can only be played, they cannot be copied.

So the only way to transfer the songs across computers is to open up a direct networking with the other computer so you can copy them across or else, copy them onto an external device or media such as a CD-RW or zip disk, etc. (When networking across macs, you will have an xtra drive that represents the other computer. So you can open it up & copy to or from it.)

To learn about how to get the songs from LW's downld folder into iTunes Music Library, see How to transfer music to my iPod (& iTunes)

Keep in mind iTunes can burn CD's! It can burn both audio cd's & mp3 disks.