I have an update on this bug. Trying v. 1.99.50.24496 (x64) and this bug persists. Whenever I change the song by pressing "next", the lyrics pane is not updated, no matter how much time passes. clicking (once) on the playlist entry immediately updates the pane and makes the lyrics appear shortly after. The same thing happens if the songs ends a new one starts, no update on the lyrics pane.
Additionally, if I'm listening to a song, but just single click another entry in the playlist, then the lyrics for that song appear, replacing the ones for the song I'm actually listening to.
To sum it up: The lyrics plugin shows the lyrics for the highlighted item in the playlist, regardless if it's the one currently playing and it doesn't update automatically when the song changes, EXCEPT if you click or double click the song.
I hope you can figure this out once and for all.
best regards!