I just realized thought of something
Did Lilly already receive her taint/stigma?
Because if I am not mistaken, if you don't receive a taint/stigma, you shouldn't be able to see the ears and tail.
Well, considering the most recent incident, she probably would have the taint/stigma now, if she didn't have it before

I just thought about it, after thinking about the fact that she has almost no relation to demons or exorcists