@Gagweeb &
@Mimik - Amduscias (the music judge) conforms to a not-uncommon trope in manga of characters who look and are generally treated male, but view themselves as female. It's more than just being a cross-dresser or gay, but I'm not sure it's quite the same thing as what we consider trans in the west, either, since it is often NOT accompanied by a dislike for their biological sex or a desire to physically change themselves. It's less an "I am a woman who was born as a man" and more of an "I am a woman, regardless of my anatomy's opinion on the matter."
While often played rather crassly as a joke (focused primarily on other characters' confusion with the situation or their discomfort at the character acting outside expectation), here the other demon is referring to Amduscias as a "lady" either (a) as a means of respecting her wishes or (b) to try and stay in her good graces.