It sounds to me like you're trying to burn from the LW playlist seen in iTunes. That playlist can be played but not copied or burnt. It simply reflects the song files in LW's download folder. So ... to get the songs properly into iTunes, see
How to transfer music to my iPod (& iTunes) & after which you should see the songs in the iTunes main Library. The library icon at the top of all the playlists is the important one.
Also, & dee232007 also, set your iTunes burning preferences to minimum speed. Some CD's don't burn reliably at maximum speed. I think the default is to burn at maximum speed so change it to a slower speed. Also check the speed abilities of your CD as a reference & choose the minimum it can burn at. Another wise thing to do is get decent brand CD-R's. The really cheap ones are definitely not reliable for playback & can give distortion in background or not play back all songs. The cheap ones tend to age quickly too. eg: after 6-12 months deteriorate in listening quality. Thus, best to pay a little extra & get good brand CD-R's.