I think that Lucius is the Prince Fernan (?) from the rumors. That prince already got her Mother's approval, so it's unlikely that the rumors are true. A mother like that wouldn't give her child away to a trashy man. She also probably told the prince that she sent Alicia to the Academy (I think he figured it out in their second year and that's why he became nice to her)
Also the people from Student Council won't fall out of love because from what we see, one fell because Alicia accepted him and the other one was for Alicia's kindness.
But this is just theories, so eh.. Thank you for the translations, by the way.