Adrian is frequently seen with his sister, Courtney. It is not known if Adrian's last name is "Lane" or if he uses his father's name as his last name. Furthermore, it is not known where Adrian resides in the birth order of Summer's children, or if he's younger or older than Courtney.
He is most likely the male child of Summer seen in Lane Miserables. It is implied that Summer's children keep running away from her but the police eventually bring them back or that she manages to relocate them.
In The Daria Diaries, a postcard from Adrian and Courtney can be found among the collection of postcards on several pages. It reads, in part:
We're saving up, and we'll probably be home for some holiday. Say hi to Mom. The card is obviously written from the Petrified Forest, located in northeastern Arizona.