you don't do the final paper work until you pick up the car. if the lease program is better at the time of delivery, you can actually use the new lease program (money factor, incentives, etc) instead of the one you originally agreed to. the dealer still makes the same amount of money on the sale so they don't care. at least my dealer doesn't.
you will get two documents. one if a lease agreement that shows sale price, down payment, due on delivery and monthlies.
the other document shows options you chose for the build and
production number. for reference, here is mine (private info redacted, duh)
View post on imgur.com
the red squares show where the production number is, which until your car is manufactured, serves as your car's identifier.