Auto lease buy out or lease pay off are the same thing and just another type of auto financing. It is the option the leasing customer has either before or at the end of the lease to purchase a vehicle instead of returning it back to the dealership. There are two types of lease buyouts: Lease end buyout and early buyout.
Lease end buyout occurs at the end of the lease and can be a good option. It is based on the residual value of the vehicle and the financing terms. Keep in mind that since you are buying your leased vehicle, you can try to negotiate a lower value and lower your payments. The dealer would rather sell the vehicle to you and save time and money wholesaling your car than keeping it as inventory. Also consider how much you would pay for a used car of the same quality.
Early buyout is a more complex process. The value of the vehicle is a combination of residual value plus the amount you still owe on your lease. The way it is calculated may actually increase the cost of the car. Because of these drawbacks associated with early buyout, is almost always better to wait until the end of the lease before buying.