Lecturer Kathy is a female teacher in the Betancria Academy of Magic, who was (in)famous among the students, due to her masturbating habits. Some of Kathy's students, (one of whom was Dan Addams) even have found a way to sneak to the Lecturer's Kathy room on the teacher's floor in order to spy on her while she was pleasuring herself after classes.
The Princess never actually meets Lecturer Kathy and only learns about her and her habits from Student's notes during Pia is Missing quest. During this quest the Princess can also visit Kathy's room and find Lecturer Kathy's Dress.