Whats the technique for levelling an uneven lawn?
I think I would choose your first option. Then, I would get some sand and apply a thin layer of it over the soil to encourage the grass to cover the bare areas. I don’t know where you’re from, but down here in Texas, it’s time for fall fertilization. If you were to just fertilize once a year (you really should fertilize three to four times a year), fall is the most important. Choose a fertilizer with a low nitrogen and make sure the potassium (last number) is the highest of the three. Down here, a good one is 8-12-16. Good luck with your lawn, and I hope this information helps.
