@cassandra827
Deep down, Lyon is still that little kid that craves affection, and he's probably the warmest person near her besides that maid, so it's completely understandable that she'd want to get close to him.
Baek Han was the first person that helped her without asking anything in return. Even if rescuing her was a coincidence, it doesn't invalidate the fact that she feels grateful for it and that he burned half of his fcking face for her (I bet she feels guilty for that).
Besides, I doubt she thinks he specifically went back just to rescue her instead of her brother. She most likely thinks he pitied her (I'd wager that's the reason why she never asked why he did it).
Despite that, I'm sure she still has feelings for Dowun. She keeps snubbing him because she's afraid of getting hurt again by his coldness. Completely understandable too imho.
Regarding Baek Han's treachery, he was always walking beside the prince like his shadow, so they must've been together when the fire started, which makes me believe he went back
after making sure the prince was safe.
Baek Han was shown to be selfless and caring towards others (for example, when he asked Lyon to spare the old lady as well), so I wouldn't be surprised if he decided to go back during the fire simply to help whoever was in need.