The lessor will assume that everything is airworthy and has been maintained according to FAA regulation. Complying with ADs will be your responsibility as the operator. Furthermore, most leases stipulate that the operator is responsible for compliance with all mandatory service bulletins as well. Where you'll likely have to pay up is if the aircraft has been abused. If seats are broken, or the chairman's nephew wanted to see if permanent markers really are, you'll have to pay.
Many lessors say they count on reragging and repainting airplanes coming back off lease.
Either way, the lessor should have accounted for his assumption in calculating the residual value on which your lease payment was predicated. If your airplane gets banged up and a 337 goes into its log, the lessor likely will expect you to pay him for the detriment. One lessor described a situation in which a business jet was damaged by a fuel truck on a ramp. To qualify as a tax lease, the lessor has to bear both the rewards and the risk of ownership. In truth, however, lessors work hard to mitigate their residual value risk on the back end of a lease.