For what it's worth, I was offered a similar deal and went for it for the reasons others had mentioned. I know this car, I have treated it well. Also I had a little bit of cosmetic damage (paint scraped off the bumper) which doesn't bother me, but I would have to repair it before ending the lease. Although it's a minor thing, the costs can be quite high to repair it correctly. In my case, one would have to either remove the battery or more likely the bumper in order to bake the new paint without damaging the battery.
For me, I never want to go back to a gasser (yes, my wife's car is a PHEV - but mine doesn't have to be as well). So my options for EVs were basically:
1) buy out my old Leaf
2) lease a new EV for 2-3 years
3) buy a new EV
4) return the Leaf and look to buy one used
Option (3) was out immediately - with the Leaf 2.0, Bolt, Model III just around the corner, no way would I buy a new first-gen EV. It would just depreciate too quickly.
Option (4) was out as well due to the high risk. Not knowing the background of the car, or really where it spent much of its life, I didn't feel comfortable with this option. I did look around, and there were really no used Leafs nearby at the time. So I would have to drive and/or fly out of state just to find a used Leaf. I would never buy a used car sight-unseen. And then I would have to ship it back, or take a long tedious drive. This may be an option for you, though, if you find used Leafs nearby.
So my options were down to (1) or (2). I ran the numbers and if my car depreciates to $0 (it won't), buying out my lease was only slightly more costly than leasing a 2015 SV for 3 years. But I have the benefit of owning it outright. If I really want to upgrade to a new EV in 1.5 years, I can easily do so. On the flip side, if I want to wait for another 5 years to upgrade, I can do that too. With another lease, I was forcing myself to make another decision in 3 years from now.
So if your car works for you, and will continue to work for you as the battery ages, run the numbers. You may find that you are offered a much better deal than you realize, especially if you are comparing to used prices.