Can a car dealer ask for a co-signer after the lease contract has already been signed?

If credit worthiness has failed, for whatever reason, then a car dealer may ask for a co-signer and renegotiate the contract. This is because if the person who leased the car failed a a credit check or didn't pass minumum requirements on their credit report, then there is likely no consideration for the contract and the contract fails. If the dealership cannot obtain an approval from its "backer" for the loan due to your failure in credit, then the contract must be re-negotiated as far as credit is concerned and who will back you in the event of default.

Credit worthiness is a creditor’s means of measuring a person’s fitness for repaying debt obligations. Basically, it is a number, called a “credit score,” that will tell someone who is considering loaning you an asset whether or not you will be likely to pay back the debt. In the case of a car lease, the dealership is responsible for verifying your credit worthiness with its financial backer. If your credit score or credit report are too low, then the backer will not consider you credit worthy and will reject the application. Sometimes the process of verifying credit worthiness takes longer than the time you are willing to wait at the dealership.

For institutions offering to loan you something, the backer is typically a bank. For example, a car dealership takes out a loan to purchase the vehicles on their lot from the manufacturer. After a sale, the dealership repays that portion of the loan to the backing bank. Because the dealership is backed by a bank, the bank has discretion to approve any loans car leases since it is their loss if you fail to repay.