The LW Playlist that shows in iTunes is simply a reflection of what audio files you have in your LW Download folder. However, the files may be duds, corrupt or even pc viruses. Check some of the music topics here MAJOR TOPICS for Upload/Download HELP. Also see the link to junk file sizes.

When you say Library do you mean iTunes Library or the LW Library window? Songs will not be added to iTunes Library unless they are added. Two main ways of adding for mac. One is auto importing which means as soon as you complete downloading a song file, iTunes will open & add the file. You set this in LW preferences under iTunes. The other technique is manual adding of songs. Manual adding of audio files is described here How to transfer music to my iPod (& iTunes) {click on link}.

BTW iTunes cannot play WMA, mp3Pro, Ogg Vorbis, or Real files.