Do we need to call and let the lender know we're moving?

[endisnear]

We found a place to rent, get the keys 9/1. Our NOD is up, but haven't rec'd auction notice yet. Do we need to call the lender and let them know so they can get the keys and note the condition of the property upon us vacating so that if there is any vandalism after we leave, we'd not be held liable? Can we cancel our homeowners? Its imponded so Im not sure if the mtg co has still been paying it or what...