I have a serious pair of questions. One, what was it that Mythros was going to ask of Lucette in Rod route, and two WHY ISN'T IT POSSIBLE TO DATE MYTHROS!??! HE IS SOO FREAKING DARK AND HAWT AND I NEED IT!!
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About your first question ... you can figure out what Mythros wanted Lucette to do by the events of other routes.
Personally, Rod is my favorite match for Lucette, but his route is the most romance-focused and least plot-focused, thus his route still leave some things unexplained. That's why the developers recommend that Rod's route should be the first one to be played