For a majority of songs. If you know the few songs the singer did write, feel free to put them down, or to add a stories involving this process. Geezer Butler wrote almost all the lyrics for Ozzy in Black Sabbath. But Ozzy would come up with the melody. Bernie Taupin mails the lyrics to Elton John, and he does the rest.
Roger Waters wrote every song except 3 for David Gilmour of Pink Floyd (Childhood's End, The Narrow Way: Part 3, Fat Old Sun) while they were in the band together.
Ken Hensley wrote most of the lyrics David Byron sang in Uriah Heep, although Byron wrote some of them.
In Phil Collins's first few albums/tours as lead singer for Genesis, he sang lyrics mostly written by other band members (mainly Tony Banks). This started changing around Duke.
Black Flag guitarist Greg Ginn wrote a large majority of their lyrics, regardless of who the singer was (yep, even during the Henry Rollins years).
Well he certainly didn't rely on, but Jim Morrison singing Robby Kreiger's lyrics did turn into some of the band's biggest hits.
Glenn Tilbrook is singing Chris Difford's lyrics in Squeeze. Liam Gallagher was singing Noel Gallagher's lyrics in Oasis
Tony Hadley from Spandau Ballet - every song written by Gary Kemp Suppose the girls from ABBA would also qualify,not sure but think most of the lyrics were written by Benny and Bjorn
Jonathan Daniel , the bassist for Candy, Electric Angels and the Loveless wrote all the songs, except one on the Electric Angels album which was written by the singer, Shane... Andy McCoy from Hanoi Rocks, the singer, Michael Monroe had a few co-writes here and there... The Damned, on their first album, the guitarist, Brian James wrote everything aside from one song written by the drummer...
Fergal Sharkey had John O’Neil to thank for for the majority of wonderful Pop Punk songs he sang in The Undertones.
You are right. On the first Depeche Mode album Speak & Spell the music is by Vince Clarke. I tend to forget this record (in the context of DM).
Bill Stevenson, the drummer, writes a lot of the lyrics Chad Price sings with All and Milo Aukerman sings with the Descendents. Karl Alvarez, the bassist, writes lyrics for these bands too.
From 1980-1986 Freddie Mercury sang around 25% of self-penned lyrics. The other 3 members bringing in their own compositions for him to sing or perform themselves. From 1989-1991, the band shared all the writing credit.