Commercial apple juices are composed mainly of sugar and water. In general, I don’t endorse sugary drinks for infants and toddlers; they encourage a sweet tooth and reduce the appetite for nutritious foods. Also, when imbibed in excess they can act as a laxative and cause ongoing diarrhea. Of course there is no need for strict prohibition; a little diluted apple juice isn’t going to turn Lucy into a sugar junkie. But there is nothing wrong with giving kids plain water.