This plugin displays lyrics in the visualization. It also looks the lyrics up online. It's a plugin is made for WinAmp so it might work with MM, I haven't tried it.
I would also add the ability to put any lyrics from the "song information" tab into tags of a song. This way the feature would work both ways.
While we're at it, I think a setting like "Always store lyrics in song's tags" would be nice too. Without it, you'd just need to accept each and every lyric manually (by selecting a provider in the "song information" tab for example). With it on, Clementine would do this for you (if there were no lyrics previously in the tag of course).
Sounds like you're talking about an Addon? MediaMonkey can already retrieve and store Lyrics in the files metadata (Tools > Options > Metadata Lookup).