For some reason recently I started thinking about all the bands that have singers who are not the predominant lyricists:
Rush (Neil Peart for Geddy Lee)
Oasis (Noel Ghallager for Liam)
Black Sabbath (Geezer Butler for Ozzy, I didn't know this until recently)
The Who (Pete Townsend for Daltrey)
Elton John (Bernie Taupin)
Elvis really didn't write lyrics but there were various songwrites for his stuff. Jim Morrison didn't write all the lyrics in The Doors. I know Robby Krieger wrote most of Light My Fire and it was Morrison who added the funeral pyre stuff.
I know I thought of more but that's what I came up with so far. Can anyone think of others?