There is some confusion between all of the people that have been asked (i.e. dealer, finance company, etc.) and it is coming down to semantics. If you terminate early, you DO pay the remaining rent on a lease. This is because the term “TERMINATE” means, give the car back and walk away before the agreed upon term of the lease. This is in your contract. It is a clause to keep you from just giving the car back to the back and walking away, which they don’t want to do because it takes alot of work and money for banks to sell your car - they are in the lending money business not the owning cars business and terminating early does not allow them to make money. So, when you ask the lender “what happens if I TERMINATE early” that is the response you will get: you owe all remaining payments including rent charge. However, if you ask them for a payoff, it does NOT include the rent charge. Rent charge is the equivalent of interest and the bank will not charge you for interest (read rent charge) they have not earned. This is why your payoff is not the same as your residual plus your remaining payments.
So, to answer the OP’s question and for all others that are confused, you CAN come out ahead if you lease, take the higher lease cash, and then call the bank to payoff the car (and own it - i.e. NOT TERMINATE and walk away). However, you will probably lose one month’s rent charge and the bank acquisition fee, which will eat into your gain. Also, it’s a pain in the ass. If you are planning to pay cash already, then it may make sense to lease up-front, take the lease cash and then payoff the loan when you get the first payment (IT WILL NOT INCLUDE ALL RENT CHARGE). BUT, if you are planning to finance after the lease, then it probably will not be worth the headache.