Most of my experience in songwriting is as the composer - not the lyricist. But I've learnt a thing or two about this creative process in my time.
A song is like any other piece of art in the sense that it must conform to its own uniques set of rules. The rules can be as sedate or bent as you like, but it is to them which the song must be true. So much more so than to musical conventions or rhyming schemes.
For me, writing a song is like creating a coherent fictional world. It has to make sense according to the rules the very gods set out for it. This applies to both the lyrics and the music - although these can worship at the alters of very different gods: the one sparse, the other intense; one crass, another poetic.
As a guitarist (as pictured in my youthier days) I build songs around guitar lines, whether complex or simple. And as soon as I start, the gods are watching... suggesting... ensuring consistency even through the rhythmic changes and sometimes illogical yet coherent chord structures.
Because a world is being built around those lines. The lines are the world. The world is the lines.
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This is one area of writing I want to develop, because it's a place I can bring my passions for music and words together. And as I write this I can sense that part of me, long dormant, which is still hungry for this place, to create these worlds in which to play; to hammer and beat the words and music into the air and seas of a far away place; the rhythms and rhymes into its earth and trees.
And by so doing join the ranks of songsmiths who write the sorrows of a world away.
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Picture courtesy of 
@ryivhnn