Elizabeth was the youngest daughter of Elliot and Kathy and the twin of Dickie. Not much is known about her as she was never the focus in any episodes as much as Kathleen, Dickie, Maureen, and Eli were. There's a few things about Elizabeth that did come up.
When learning how to write, Elizabeth used to write her letters backwards that her sisters did not used to do. She was learning how to play the piano.
When Elizabeth was 15, her old grade school picture somehow got uploaded to 'Pediphax', an online web site for pedophile; it had a motto "look but don't touch". After Elliot and Olivia questioned the webowner, Jake Berlin, for his knowledge about the case; Jake was attracted to little girls but knows the law and he put the picture up to set Elliot off into assault. He beat Jake up and tried to get Elizabeth's picture off the site himself. Elliot couldn't do it- he needed the password- so Don Cragen ordered Jake to take down the picture. Jake wanted Elliot arrested and to press charges. Instead, Elliot went on unpaid leave until his and Jake's wounds heal.
Elizabeth took part in her school plays; Elliot attended the opening night of "The Diary of Anne Frank" and was going to be in another one that Elliot nearly missed. With Elliot's help, Elizabeth got a job at Target.