Car dealer made a written offer for a monthly lease, buyer put down $500, when buyer arrived to sign contracts dealer raised price $100/month.

Without a COPY of the offer that you took with you, all you can do is demand your $500 back TODAY, not in the mail, and not tomorrow. Or you will complain the the state dealer licensing division, and the AG's office.
The offer might have had contingencies, such as a credit check, and a time limit. Most likely your credit score isn't good enough for the quoted price.
You should have waited to put down a deposit.

Generally a written contract is binding. You have all the elements, an offer, an acceptance, a payment. But without reading the contract, we can't be sure if there wasn't a loop hole the dealer could use to raise the price.

What ScottGem said, except that OP mentions buyer arriving "to sign contracts". If the offer made by the dealer was accepted by the buyer by making the down payment, it's unclear why further "contracts" were needed. It could be a tentative lease, subject to contingencies such as those joypulv lists. As noted, one would have to review the terms of the dealer's written offer.

Did you ask him why it was a hundred dollars more? Did you sign the new contract anyway?

From what I remember of car buying, There usually is a lease contract that has to be completed. So what the buyer received may have been just an offer and that's why they needed to return to sign the lease.

Additional fees and taxes may have applied.