When you write it in a letter/conversation form, do you listen to the music while doing it? Or do you just write it out and go from there?
Often it comes about with a specific lyric that seems to naturally fit a specific piece of music--we'll call that "inspiration" (for lack of a better word, not because I in any way think I've got divine intervention going on in my songs). Either while playing a progression, vamp, etc., or listening to an older segment of music, I think of something that just fits. Generally, though, it would be just a fragment. Then once I have that, I think about that word or line and do the rest of the music. I very rarely would consider a piece of music done until I have finished both lyrics and music, as I don't like to have to cram either one to fit the other. I am more likely to get that first "inspired" combination of music and lyrics, and then build the song around that using any number of possibilities.
For example, I once did a Latin-tinged chord progression that went as below, with each chord lasting four beats and particular emphasis on 2 and the and of 3:
iii-7 ... V13/ii ... Vmaj7/V ... v-7/V ... V13 ... Imaj7
As I played that relatively slowly--actually thinking about Queen's "Who Needs You," which sounds nothing like what ended up happening--I decided I wanted to write a song that was sort of filled with some mock bragadoccio--Freddie Mercury, you know, always going off at the mouth but tongue-in-cheek. So I ended up singing the line:
"Nobody believes me that my old girlfriend was a beauty queen, but she was. Well, she was."
That was my in. I knew now I would be sort of passive-aggressively bragging to my audience that I had dated a beauty queen, and yet come across as pathetic, as any listener would think, "well, even if that's true, who cares? You aren't anymore, and yet here you're obsessing about it!"
So with that idea, I repeated that chord progression while coming up with other possible lines. These would be verses (although plenty got thrown away). I decided I only needed one other musical segment to this song because it was kind of a one-joke song. I didn't want to belabor it. So I did the words to a refrain, then music to match. But if I would've had music done on that latter segment, I would've first thought, 'what do I want this segment to do?' I might even have written it without considering the music, or even necessarily writing real lyrics--just the point of it. Then I'd pay attention to the music again and decide whether I could say what I meant, or even certain words and phrases that were evocative of the idea.
Anyway, summary and directly answering the question: yes, I'd listen to the part that really initially hooked me and write around that. Then I'd take it away and write based on the lyric, then return to the musical ideas and see if I could make it all work together. But I'd try not to force it--I'd rather change the lyrics or music than smash them together.