In the case when a auto leasee dies does contract end?

Depends on who signed the contract/loan. Typically, when the leasee dies the contract does not end. Though, the dealer should be informed so all information can be updated (ex. car registration, etc). If it is left alone and falls into default, the dealer or loan company will reposes the vehicle. If there was a co-signer (spouse) then they will go after the spouse for monies owed. If your interested in keeping the vehicle you can call them and tell them you're interested in buying it, then just make an offer, they'll probably be glad to make a deal rather than get stuck with a car they can't sell or go through the hassle of the probate lawyer and waiting for funds.