DesktopLyrics is an application that displays the lyrics of the song currently playing in "iTunes" right on your desktop. The lyrics for the song have to be set in iTunes, DesktopLyrics does nothing to fetch them if they aren't available in iTunes. If you don't want to type-in all your lyrics manually you can use an application like "Harmonic" .
This is what I was looking for. The transparent window is in fact the big advantage. The developer should add "launch iTunes automatically" to Preferences to make the application even better. (Version 1.0.1)