Chapter I Black Order

Luna's Innocence makes her look like a 20 years old girl, even though her real age if far older than that.
Apart from making her body not age, her Innocence makes her can read what other people thinking. in other words, she can read minds including knowing whether someone is lying or not.

With her innocence ability like that, she couldn't use innocence to fight Akuma physically. Her ability is more often used for interrogation, including the exorcist who just joined.