"Without melody there can be no lyrics"

I disagree. Lyrics are simply words. Whether they are set to music or not has nothing to do with their classification as lyrics. Of course all music has a melody and most lyrics follow some sort of meter, but the melody doesn't make the lyrics, nor do the lyrics make the melody. I'd be willing to bet that the majority of spoken word had lyrics written before a melody. A prime example would be La Dispute's "Here, Hear". Each of the tracks from the first two EPs are actually based off of previous works of literature. Are they still lyrics? Yes. Where they created for the music? No, quite the opposite actually. With or without a melody, lyrics are just poetry.

Really, what you write first all comes down to what the focus of the song is. If you're writing something centered around lyrics then lyrics will probably be top priority. If you're writing some twisting crazy math rock then lyrics are probably second in line. I don't think the point is to create lyrics for a song, or the other way around, but rather build off of what you've already created. Write lyrics and when you find a melody that fits, use it. Write melodies and when you think of words that fit, use them. As someone else said, keep the momentum going.