So there seems to be some misconception floating around the internet that it is impossible to sell a leased car. I guess technically that is true, since the leasing company owns the car and holds the title. But you, as the lessee, can certainly arrange the sale of a leased car without much issue.
Last December, I leased a 2016 Chevy Cruze Limited for 24 months for $0 down, $85/month. About a month after I leased it, someone told me I could sell it to Beepi for a profit. I was like “WUT?! You can sell a leased car??” and decided to check it out. Long story short, Beepi bought my leased Cruze for $18.7k (payoff obligation was 13.7k), so I pocketed a cool $4k selling my Cruze. That on top of the $700 Costco gift card I received, and $300 in Visa gift cards from the dealer I leased from. All I ended up paying for that Cruze was 3 months of payments totaling $255 plus another ~$120 for insurance. 
I leased another car, a 2016 Spark EV, in May of this year, hoping to do the same thing I had done with the Cruze a few months earlier. However, Beepi had changed their appraisal strategy, and so I wasn’t able to successfully sell my Spark through them.
Not only that, but the $2,300 MD EV tax rebate I had been expecting to receive was denied, leaving me with a leased car I didn’t need that had 35 months of payments left. Crap!
I contacted the dealer I had leased it from, and through some nifty negotiations, I was able to arrange a Spark EV swap (out with the green one, in with a red one) and come out ahead. Even with the negative equity rolled in from trading in the old Spark, I was able to lease a new Spark EV for $0 down AND a lower monthly payment ($148 instead of $150)! The dealership agreed to give me $13,500 as trade-in value for my green Spark. So leased vehicle #2 was sold to the dealer.
However, this still left me with a leased car I didn’t need (though in a better position that I was in with the first Spark)!
What to do? List it on Ebay! I created an Ebay Motors auction for my 2nd Spark EV, and managed to find a buyer that was willing to pay an amount equal to the payoff obligation of Spark #2, and $100 bucks to me to boot. All I had to do was arrange a 3 way call with GM Financial so the buyer could get the payoff information. GMF sent me the forms I needed to fill out, I scanned and emailed those forms to the buyer to finish filling out, and then they sent the payoff check! GMF will send the title directly to the buyer in 1-2 weeks, and the buyer has just arranged the shipping for the car. All I need to do is be there when they come to load my Spark EV up on the truck. 
So while it is very rare to actually profit from selling a leased car, it is totally possible. Just need to be savvy and negotiation.
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