Typically we do it as it comes (writing book, then pausing and doing lyrics when I hit a song!) If we do end up writing one first, I'll typically write the lyrics first (because it takes time for Elliot to turn those lyrics into a song, which is time I can take to write the book; and because generally book is easier to rewrite than lyrics because of the less strict stipulations on timing, rhyme, etc) but that's not really best practices, haha.
The rationale behind this is that, ideally, your songs should be moving the story forward, not repeating anything from the scene, and giving us a greater understanding of the characters. It's never worked in my brain to skip over songs because I find it difficult to imagine the new state of the characters (what they've said, what they've thought, how they've changed) before I've written the song in which that happens.
If you do write one before the other, I recommend writing monologues for each song that contain granules of information you can mine for lyrics when you do go back and write them, and changing the book around those monologues once the songs are written to remove redundancies and make the songs feel like they launch you out of/into the book effectively. Not saying my writing always does this -- especially really old writing -- but that's why I write in the order I do!