She doesn't really put herself as an authority figure anywhere. In canon, people place her in that role. Humanity made her their saint, Cain, Seth, and Abel made her their mother, etc. She's always playing the humble doormat until something big happens.

Well if she is pinged by one of his posts, she'll just be unbelievably nice to him like she is everyone else.

Haha yeah. If you think Claire can regenerate, Lilith is even worse. She doesn't react to threats at all either.