Cody tells the kids that the new baby won't have to worry about if it is a Foster or a Lambert, it will be both. This isn't true since Carol herself isn't biologically a Foster. That was the last name of her first husband. In the first season, Carol's mother and unmarried sister are featured, and their last name is Baker. This would be Carol's maiden name, so the baby would be a Baker and a Lambert. Once the baby is born, they are told her name is Lily Foster Lambert (supposedly proving Cody's point.) But it makes no sense for Carol to name her baby after a husband she divorced.