My tenant messaged me this morning stating she locked herself out of her bedroom. I previously lived in this property and never locked myself out of my room so I never looked nor do I even know if I have a key for the bedroom door. I told her this simple fact and stated, "unfortunately I would recommend calling a locksmith." 
Hours later she sends me the bill and says "He had to put a new lock in due to something with the door."
I was never called and asked if it was okay to put a new handle on the door. In my head, the lock smith was just going to open the door for her. 
I responded, "Thanks for the receipt. Since he had to replace the lock, I am willing to reimburse half of the cost. "

Which initially I was expecting to pay for nothing. She then responds, " I would like the full refund. This was not something I created. The door has lock which has no key for the lock. How am I responsible for even half of that? It's not my door or lock. If I put the lock on the door, I would not ask for you to pay half. "

I'm at the point where I've gotten out THE lease and it doesn't have anything about locksmith, however the maintenance, repairs section states, " All normal repairs necessary to maintain premises in a tenantable condition shall be done by or under the direction of the landlord, and at the Landlord's expense, except those caused by negligence or acts of the Tenant, which repairs shall be made at the sole coast of the Tenant. 

The bill was $135. It's not about the money. It's about the principal and setting standards incase a situation arises in the future. Am I at fault because I don't have a key for my bedroom door? And/or is she at fault because the locksmith didn't call and get my permission to replace the door handle?

Thanks for reading really appreciate any advice!