I would do this as well. And point blank tell her - you believe she is lying to you, she is actively stealing your food, tell her you are disappointed and don’t understand why and if there is a financial issue, offer her your listening skills. But be honest and tell her that padlocked safe in our kitchen is there because of your bad habits.
I’d ask her to pay 10 bucks extra on rent to cover the cost of the lockbox as well.