If you are signing the lease with this dealer, you can’t control how many pulls on your credit, and more than one won’t affect your credit score in the newer fico models.
If (for instance) you fill out the credit app today, and sign tomorrow, it’s possible it gets run a 2nd time. If your contract gets returned in a week and needs to resign, for some brands they will rerun it again to ensure no other changes to your trade-lines. As long as you only open one auto lease from these inquires, the impact is the same whether it’s 1 pull or 3.
If a dealer wants to pull credit to quote a lease, tell them to pound sand