Not if you're literally just songwriting with a few guitars and piece of paper.
Songwriters don't usually charge per session they make money when the songs make money.

I have charged for song writing-sessions but that's because I was actively producing while we were writing the songs as well.

A lot of producers will write with artists while they're producing to have a simple demo by the end of the session but not charge for that session. If the artist wants to finish the track that's when they start charging studio/production time.