Louis Perez is Los Lobos’ primary lyricist, but I’m pretty sure he rarely sings in the band.
The Band fits, as well. Robbie Robertson wrote or cowrote the majority of the lyrics, but (according to Wikipedia) only recorded lead vocals on three songs. There is some contention about this, as Levon Helm said that the songs were often composed as a band — but did he mean the lyrics, the music, or both?
Boston is another: Tom Scholz wrote most of the songs on their albums, though singer Brad Delp has a couple credits.
The example I keep hearing when I bring up this topic (around fans of a certain persuasion) is Robert Hunter, who wrote lyrics for songs Jerry Garcia sang. “They considered him part of the band,” they cry, but no.
However, it suggests a category of nonperforming lyricists who primarily worked with one artist. Bernie Taupin, of course, and I guess the other Dead lyricist John Perry Barlow. Pete Brown wrote songs with Jack Bruce for Cream and solo; Peter Sinfield wrote for the first few King Crimson albums. Jim Steinman for Meat Loaf, but that didn’t last long.
You mean as a regular job, right? And only lyrics? So you’re not looking at, say, bassist John Deacon writing Queen’s “Another One Bites the Dust” (music and lyrics) or guitarist Robby Krieger writing the Doors’ “Light My Fire”?