This has to do more with the total loss declaration than with anything else.  Although you have GAP coverage, if the car is a total loss and you own it and have coverage, you can either turn the car in and get fair market value or you can keep the car and get a lesser amount, but you can not force the insurance to pay to repair it.  Here, you are leasing, so if you turn the car in, you will be off the hook for the remainder of the lease.  But you can not force the insurance to pay to repair it.