I did a trade for my LJ: I had a 2012 JKU that wasn't paid off. I was trading for an LJ that was paid off. We had to contact my lender and his lender, and square away the details. All of this can be done on the phone.
For my deal, he paid me $2500 cash plus his bank took over the loan, and gave him a new loan.
So make sure all of the details are clear before assuming this will work. It's tricky when the vehicle isn't paid off yet, but it can still work out fine.
For my deal, my bank was a giant pain in the ass. I don't remember what the hangup was, but it was like pulling teeth to get them to send the title to his bank. It did work out thanks to me making a few dozen phone calls. Though if the seller is a deadbeat and decides 'he's good', you could have a problem with getting the title.