Kinda obsessed with your interpretation of Lizzie afton tbh. Was she always this level of unhinged or was she slightly covering it up with Little Girl Charm before waking up and fully taking on Williams...William...ness.
Excellent question
I've always interpreted Elizabeth inheriting a lot of William's sociopathic tendencies (as seen with Baby in the games being a manipulative bitch of an animatronic)
In Soldered Wires, Elizabeth is her father's daughter; she learned how to manipulate her friends into following her and giving her their best toys or presents, even at their own birthdays. And those that get on Elizabeth's bad side suddenly find their favorite things being stolen and found broken. And those who got on her worst side quickly found themselves at the hospital. (Think Azula from Avatar: The Last Airbender)
This behavior manifested well with William's spoiling of her since her birth: if she wanted something, he would get it for her; if her brothers harmed a hair on her head, he would see to it they were punished for doing so; if she got in trouble with someone outside the family, he would throw as much money to the problem until it went away. And Elizabeth would fake injuries and lie about her brothers doing stuff they weren't allowed to do in order to get what she wanted around the house (William would be in denial his daughter would be capable of such criminal activity due to his misogyny against her until her teen years)
Michael and Evan were probably the two closest people to ever know the true nature of Elizabeth throughout their childhood. Evan, being Evan, would give into Elizabeth again and again due to how much she could outfight him. Michael could at least hold his own against his baby sister and tell her no when she deserved it, but he knew she already had William in her tiny hand the moment she yelled.