I have found zonings in my city that allow billboards but the land is owned by the city. Can I approach the city regarding a lease just like a private owner?
Sure you can. But remember that, in many cases, it will be open to public bidding.
Check with the city or county. Many are raising revenue by selling city owned parcels. Assuming it's vacant land, if you make a decent offer, you may be surprised that they would sell it to you.