SO LIZZY ISN'T HER TWIN SISTER???

Nope. Her sister, Rebecca, goes by the name Anna now, and was raised in a convent. Connor finds her and they end up married, but she thinks he was hired by a stalker ex to find her and runs away from him. A year later they find her and find out she and Connor have a daughter. He brings her back to Texas, but that was as far as I was able to get in the Manga before needing to pay.