Elizabeth made Gabriel a lycanthrope by shifting at his request while they were having sex. After Gabriel is killed the other leopards initially say they miss the way things were when he was their leader, but in truth Elizabeth is the only one who truly misses him, even if Gabriel had long since grown bored of her.
Elizabeth hates Anita because Elizabeth herself isn't strong enough to lead the pard. In Narcissus in Chains she invites Micah to St. Louis to audition for the position of Nimir-Raj without Anita's consent. Because Elizabeth leaves Nathaniel alone when she is supposed to chaperone him, and continues to defy Anita, she is shot by Anita with normal bullets as punishment.