The artists may provide lyrics, but they are the ones who put the songs under copyright via ASCAP or BMI, not the labels (assuming the artists actually wrote the song). Just because they printed them on a CD booklet or vinyl insert for the benefit of fans doesn't mean that the fans now own the lyrics. This is no different than if someone put up HTML versions of the Harry Potter books on a site and placed ads on every page.
I would also draw a difference here between fair use for non-commercial purposes, and the 99% of the lyrics sites out there who are trying to make a business out of reprinting someone else's copyrighted work. IANAL, so I don't know if fair use would really cover a non-commercial site of lyrics, but I'd have a lot more sympathy for that use.
If they want to make this thing legit, they should set up a lyrics site where a portion of the ad revenue for each artists' lyric pages goes back to them.