Lucien and Daisy have barely finished declaring themselves and already discover a harsh reality even for couples who love each other deeply: they won't always agree on something.
He clearly understands how she feels about her family as he also has doubts about his mother's mysterious identity but won't be able to come to a conclusion before hearing everything she has to say in person.
So, he wants to support Daisy in finding out why her family sacrificed her without thinking even though he's pretty sure fear was the main reason her family didn't protect her from the Vampire Royalty.
He also understands that because they are near Blood Moon, Daisy would find it easy to create a portal there. But he can't agree to let her go alone into a world where there are people who probably still want to hurt her.
Daisy understands how Lucien feels about her and that situation as she understands and shares from his protective personality.