Though nominally the King of his Nation, Lucas is pretty much the very model of the "hen pecked husband" who defers to his loving wife; Polifonia is able to easily drag her husband (often literally) back to reason in his frequent outbursts threatening Kojou with death for misconstrued slights.
Though stern and proud as befitting a Warrior King, Lucas nonetheless is a loving father towards his sole daughter and the heir to his throne. And as befitting a Warrior Father, he is quick to anger when it comes to matters of her honor and chastity, and frequently threatens Kojou with (literal) military action if he even (acidentally) looks at her the wrong way.
Lucas does not hold the hatred of bastards so unfortunately common to Nobles in fiction, and rather than treating Kanon as a threat to his Throne, loves her as dearly as if she is legitimate; though his affection towards her is closer to a fatherly one than a brotherly one, as she is younger than even his daughter.
He is also as violently protective of Kanon as he is of La Fiola, and is more than willing to bring the might of his Military down on Kojou's head at the slightest implication of perversion on the Vampire's part.
Seems like he doesn't really like Kojou; having his opinion of his long[ tainted by rumors of his amorous and lustful conquest towards young women, and sees him as a (not unreasonably assumed) threat towards the chastity of his daughter La Folia and his newfound sister Kanon.