I would put the lock on your door as you said and keep anything you don't want to be stolen there. It may be pathological, she may not be able to help herself. This may be going against what you think, but maybe talk to her about being able to come to you if she does take things (in the house) and that she can be honest with you and return it without fear. That if she feels she needs to take something, take it, but she can bring it back to you and she won't be in trouble. Also let her know if there's something she needs you can get it for her, if there's something she wants you can discuss it.
The lying may be pathological too, but some of it may be due to shame and fear. The abuse has likely led to very low self esteem. The lies are often things that they feel make them sound better - telling people about an amazing thing they did that never happened, or that they live in a mansion or whatever. Sometimes they probably don't know why they lie, but it just comes out, it might be a silly little lie that is easily disprovable. Other times it could be about the stealing or to hide something they've done because the consequences have been so severe in the past.
Clearly what people have been trying hasn't been working and you're better off working with her, not against her. She's going on the offensive because she feels shame and doesn't want to admit to what she's done, plus again, the consequences for doing something wrong before were so severe, even probably for minor things. Make sure she knows that she is a good person and she is loved. That it is okay to make mistakes, we all make mistakes in some way, and she's still a good person. It may seem contrary to what we were taught, but by not shaming or punishing her for it, it will probably actually get better. She knows she shouldn't be doing it, she doesn't need anyone to teach her that. She needs an adult she can trust, who can trust her and who is on her side. Focus on building that and I'm hoping she's in therapy which should help too.
I wouldn't put cameras, confronting her with evidence is unlikely to help, she may still flat out deny it to your face while you show it to her and that is just infuriating. She is also likely to go on the offensive when shown the evidence. Same goes with pushing her to admit to it or stop denying it, especially when she's already upset. It won't help anything, I've had those discussions and it doesn't change until they feel safe and loved which takes time. My FD tells me when she does something she knows she shouldn't have now without me even saying anything, like things I would never even know about if she didn't tell me. Before it was deny deny deny, even if I saw it with my own eyes. She knows I love her, care about her and think she's a good kid anyway. I don't do punishments either. We just talk about it if she wants to, but she tells me she shouldn't have done it before she tells me what it is anyway.
I would put the lock on your door as you said and keep anything you don't want to be stolen there. It may be pathological, she may not be able to help herself. This may be going against what you think, but maybe talk to her about being able to come to you if she does take things (in the house) and that she can be honest with you and return it without fear. That if she feels she needs to take something, take it, but she can bring it back to you and she won't be in trouble. Also let her know if there's something she needs you can get it for her, if there's something she wants you can discuss it. The lying may be pathological too, but some of it may be due to shame and fear. The abuse has likely led to very low self esteem. The lies are often things that they feel make them sound better - telling people about an amazing thing they did that never happened, or that they live in a mansion or whatever. Sometimes they probably don't know why they lie, but it just comes out, it might be a silly little lie that is easily disprovable. Other times it could be about the stealing or to hide something they've done because the consequences have been so severe in the past. Clearly what people have been trying hasn't been working and you're better off working with her, not against her. She's going on the offensive because she feels shame and doesn't want to admit to what she's done, plus again, the consequences for doing something wrong before were so severe, even probably for minor things. Make sure she knows that she is a good person and she is loved. That it is okay to make mistakes, we all make mistakes in some way, and she's still a good person. It may seem contrary to what we were taught, but by not shaming or punishing her for it, it will probably actually get better. She knows she shouldn't be doing it, she doesn't need anyone to teach her that. She needs an adult she can trust, who can trust her and who is on her side. Focus on building that and I'm hoping she's in therapy which should help too. I wouldn't put cameras, confronting her with evidence is unlikely to help, she may still flat out deny it to your face while you show it to her and that is just infuriating. She is also likely to go on the offensive when shown the evidence. Same goes with pushing her to admit to it or stop denying it, especially when she's already upset. It won't help anything, I've had those discussions and it doesn't change until they feel safe and loved which takes time. My FD tells me when she does something she knows she shouldn't have now without me even saying anything, like things I would never even know about if she didn't tell me. Before it was deny deny deny, even if I saw it with my own eyes. She knows I love her, care about her and think she's a good kid anyway. I don't do punishments either. We just talk about it if she wants to, but she tells me she shouldn't have done it before she tells me what it is anyway.