Reporting damage occurring to a property requires using Airbnb's resolution tool and at the first instance the only thing you can do is send a demand to the guest who declines it and then you escalate to Airbnb who will usually ask for receipts and photo evidence and then pay for the damage.
I called the guest to explain this as soon as she told me she'd broken the key. I then called Airbnb to initiate the process. After filing the damage report, I sent another text message to the guest explaining that Airbnb would be paying for the damage. I have said text message in my records as does the guest. At no point did I try to charge the guest for the broken lock.
Was I disappointed with the damage? Of course, I am only human and it's an annoying inconvenience to have to deal with.