Idk why people are expecting any of the characters to have ideal morals, are we forgetting that Lucius did start a war out of nowhere? Regardless of the cause, wars always end with bloodshed. Are we forgetting that he called for Paulina's execution until she proved herself to be exceptionally useful? Despite everything he is, he is still an emperor and the one who's running this entire war. He had no reason to spare who he considered a very skilled enemy. It makes a lot of sense for him to end the entire royal blood line, she could have just been used as a pawn to start a coop to reclaim the throne. And he evidently does not want that.
None of the characters who attempted to rape Paulina have been punished either, they were only punished by Paulina herself in her attempts to defend herself. Which is also obviously why Paulina killed the princess herself, so that that she doesn't suffer anymore than this. There was no way that Lucius would have let her keep her luxurious life style, there's no need for a princess who's father attempted to end his life. There was no way anyone on the emperor's side would protect the princess either, she has no value to the emperor, only a source of problems in the future and not to mention those are the same people who tried to get rid of Paulina as fast as possible until Lucius went: No.