Hello there! I know my reply is kinda late (gonna try to be more active from now on)...but nevertheless, lemme share some stuff with you! Hopefully you can benefit from it.
You don't have to be a singer to compose, write, fit lyric/melody into their vice versa, etc.
So far I've only written two songs whereby the lyrics were written down first, followed by the melody. For one of songs, I first started writing on the chorus, then slowly branch out. The whole tune came to me through reading out the lyrics. The syllables will guide you on how many notes a particular line should have.
But I have to be honest, it was tough! Especially when the previous two lines have been going well and fitting, then the next line has an influx of syllables that spoils the melody and make you go "WTF!"
I will still suggest trying at least once to write a song with the lyrics first. It's an experience and you'll find it benefiting!
Alot of my friends always debate on whether which is of more importance, melody or lyrics. This is a "Personal Opinion" kind of thing. To me it would be melody, cause melody is not just about the music notes. If you look carefully at it, melody itself has rhythm. As what my lecturer told me before: "A melody is a series of musical notes arranged in succession, in a particular rhythmic pattern, to form a recognizable unit." SO TECHNICAL!!!!
Anyway, when you first try out things like song writing or even trying to fit melody into a set of lyric, you'll find it difficult, hard to understand how it works, etc. That's because we lack the experience. Once you keep doing it, you'll get the hang of it and things will be fine!
On a side note, do check out my stuff!
Do check out my works:
http://soundcloud.com/yunxiang
If you wanna know my gears and what I'm currently doing with music, do check this one out:
http://chongyunxiang.wordpress.com/