Here's a natural hair spray recipe:
2 to 4 lemons
Slice the lemons and cover with water in a pan. Simmer for 1 hour, adding more water as it evaporates. Let cool, then strain. Pour the lemon liquid into a pump spray bottle.
Makes 2 to 3 cups.
Shelf life: About one week refrigerated.
Everything else I'm finding involves gelatin. You could try using agar powder or unflavored vegan gel and try the same thing. No guarantees on that, though.
I've also heard about using aloe vera gel.