Um...even if Luxia didn't exist, that doesn't mean the Emperor would fall for her (that's the pitfall of so many characters). Thus far, the Emperor's only interest in her is the lack of fashion sense.
The switch to more bold clothing really lowers the impression of a white lotus. The way she acts don't fit the clothes at all. Then she ends up acting aggressively in a way that further implicates herself. Why bother finding the emperor if you've already got an idea of where your sister is? What a dumbass. She played herself.