I wrote lyrics without music for almost thirty years before I ever wrote a lick of music. I've written every way there is to write in terms of what came first.
I've written lyrics (often) to someone's existing instrumental (always with permission).
I've written lyrics, then melody, then music.
I've written music then added lyrics.
I've written vocal melodies, then added either music or lyric.......
I've sung existing songs to an alternate vocal melody still following the beat and structure of the original, then written new music to the new vocal melody, then written new lyrics.
I have no CLUE why someone would restrict themselves to writing the same way every song. Not only would it feel terribly limiting, but it would get boring for me if I did that.