I Saw the Devil
It is possible that demons can posses people in the moment of weakness. The singer in the anime got possessed cause she realized she wasn't getting famous fast enough and it made her easier to manipulate. By the time she realized what she had done it was already too late.
Lady might be strong and knowledgeable of demons, but she probably still has moments of doubting herself. It can start with a whisper that seems to come out of her head, and as it gets louder so her mental defense gets weaker until the moment is right. Of course, if this is the trick the demon uses, then possessing her again once she knows what's going on is impossible.
Maybe, but she's been in the business for a long time by that point. If she knew that was a possibility what has prevented her from falling victim at times when she was feeling weak? Why this time? Because, plot. That's all I can think of. Chances are we can make better speculations than they reasons when I'm sure it didn't occur to them to explain a how.