You can't just have the rest of the lease erased, etc. for going into another. The ONLY special thing that can happen, and that's common with GM, is a lease pull-ahead offer that will let you get into another new GM vehicle in the last 1-6 months of the lease, rather than the very end. Not before.
Otherwise, trading in a leased vehicle is just like one that is still financed, and you'll be responsible for the remaining portion of your lease and then also the residual amount--it basically has to be paid off, just like if you wanted to buy out your lease.
There's really nothing special that can be done, and especially not on the part of a dealer, aside from the lease pull-ahead offers near the end of the terms.