My theory is that our boy Noah is the heir to the Empire since they stated there is no known heir and the princess is currently engaged to someone old or ruthless that the prince who Lucy is trying to get away from is currently looking for a solution.
So I'm assuming that Noah is the ML and heir to the Empire based on all the details they're throwing at us. After all it's good writing to only use what's necessary to move up the storyline unless the purpose is to confuse us.
What I don't really get is how the younger brother is allowing the ogfl cousin to hurt him when the brother has a higher status but that's bullying I guess. Still weird imo for no one to say anything to the dad or older brother about it since it'll look bad on the Duke family. I do wonder how both girls were able to enter into this universe