That's correct. You share a great deal of my interpretation However, in that world, Lucio is somewhat kinder to his student, Valentina. That aside, it is true that he a strict teacher, but he is not coercive. (At least when there is no outside gaze) But after the disciple died…
@Haeticket I believe if their roles were switched Valencina would be young ambitious student striving to get to the top of hierarchy who easily loses her temper
While Lucio is calm and efficient master who's tired of his duty and responsibility but does what he ordered without questions