Lying isn't a healthy behavior. So, I don't think a therapist would lie. Though I'm not sure what kind of question you're thinking of.

Should a therapist lie? Probably not. Are they allowed? I'm kind of stuck on this. "Allowed"? Allowed to lie to the client? Allowed to lie to another provider? It would be a mess if they did. I can't see why one would lie about that.

Lying about treatment. Again I'm stuck on what kind of question. I can't think of a reason a lie would be necessary but maybe I'm missing something.