Since VW still requires you to maintain all lease terms, it's likely VW will require the registration is caught up to current before you turn it in to cancel the lease. The state will want their money, and your state will likely have a penalty for late registrations as well. You might be able to take care of it at the dealer when you turn it in. My guess is it will delay your official turn-in date until this is cleared up because VW will not take possession until the registration is valid and current. The gap will show up anyway when the vehicle is reregistered back to VW when the transfer paperwork is filed with your state. Your state might allow the non-registration if you can provide proof the car was not driven on roads during the time period in question, but I think that will be impossible for you to do.
The problem I see in your case with VW is since it wasn't currently registered in your name, VW can't validate you had possession of the vehicle since Sept 2015. Even though likely not allowed in the lease terms, they could assume you had sub-leased the car to someone else, who paid you the lease and insurance amounts for you to make the payments. Lease and insurance payments don't provide validation, only the state registration does.