How can I view iTunes metadata lyrics without using Get Info in iTunes? I want a third-party application which will show me the lyrics I've entered in my songs' metadata, preferably without a dock icon. Either a pop-up of some sort or displaying them on the desktop would be acceptable.

I've tried Get Lyrical, but I don't want something that will search for lyrics automatically. I can't use Cover Version, as it purportedly doesn't work on Lion. LessLyrics/LessDJ doesn't quite fit my needs, as I'd rather have something a bit less visible.

Another possibility, and just as acceptable, is if there are individual files stored with the lyrics of the currently playing track. That's unlikely, but please let me know if it's the case.
Have you tried Lyritop? It's an app that displays the current iTunes song lyrics on the desktop. It does display a dock icon. You can also adjust font, size, position, color, shadow, etc.

There are no individual lyric files that are stored on your computer. The lyric information is embedded in the id3 tag of each song file. There is an app called MP3LyricsExtractor that will batch extract song lyrics into individual text files.