If it's a good deal with adequate miles left look into the swapping sites. Otherwise you'll have to pay the remaining payments and disposition fee when turning it in.
I am in the auto sales industry. I can help a lot here. There are a couple quick questions. How long was the original lease term and how much time is remaining? Next, and I mean this in all seriousness. Go to KBB or NADA and check the trade in value for your vehicle. Plan on the worst case scenario. Imagine the dealership will only give you a number at the middle of the trade range for "good" condition. Then look at the priginal leave paperwork at your "Residual" amount. There are a few versions of how the process can move forward from there.
1) If the Residual amount is higher than the trade amount, you can:
a. Keep making the payment as outlined in the contract (follow the original agreement)
b. You can turn it in and still be liable for any monies that you would have owed according to the original terms. (This is more like voluntary repossession, and caries with it all the negative impact)
c. You trade the car in on something more affordable and get 45 days until your next payment is due. If you find something with rebates/incentives that bring down the purchase price, you can absorb most/all the negative equity.
d. You can private party sell the vehicle for the remaining cost of the lease+taxes+residual amount. Pay that money to the company. Get title for new owner.
2) If the Residual amount is lower than the trade amount, you can:
a. Sell the car to the dealership. You don't have to trade-in for a purchase on a new vehicle, but they have to actually buy it from you instead of ground the lease.
b. Trade in on a newer and more affordable vehicle.
c. Private party sell it and keep your profits while paying the velicle off. All sales tax requirements on the remaining balance of the car must be paid for at time of purchase/registration. This could be quite expesive as you very likely would owe a couple thousand additional dollars on top of the proces.