Snarking among bitches is common. Zoe has been queen of the roost since she can remember. It's difficult for her to give up what she sees as her territory. If they are already playing together most of the time, they should be able to settle in together. They have to figure it out between themselves, but if it looks like someone is going to get hurt, you will have to intervene.
If your son has a crate for Lizzie and you have one for Zoe, if they appear to be on the verge of murder, I suggest you crate them both so it doesn't look like one is favored over another. That is your message that you, as leader, will not tolerate that sort of behavior from either of them.