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) [i]looks[/i] at her the wrong way.
Lucas does [i]not[/i] 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 [i]violently[/i] protective of Kanon as he is of La Fiola, an is more than willing to bring the might of his Military down on Kojou's head at the [i]slightest[/i] implication of perversion on the Vampire's part.
Seems like he doesn't really like Kojou; having his opinion of his [i]long[/i] 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 Fiola and his newfound sister Kanon.