[Mornai]

I think he didn't tell anyone because he's not truly an evil man. He's sort of a hardass and a bit full of himself, sure...but in the end he's just trying to protect his daughter. Knowing that there is a man who committed murder before the apocalypse close to you at all times is a decent enough reason to at least be cautious(the extra hostility is probably his natural self).

Perhaps he kept it secret to use as blackmail, but it's obvious he didn't care for Lee and did not want him in the group, regardless of his capabilities. He says this himself in episode 2. "Ah, stuff all that. We'd be fine without you."