Bike-chan
From Serial Experiments Lain wiki
Bike (びけ Bike), Bike-chan is a toy dog owned by Iwakura Lain that is unsuccessfully automated by her an unknown number of times. It appears in the manga and the game. Lain has reportedly owned it since birth, although there is no way of knowing how many incarnations it has had.
Trivia
A stuffed toy dog closely resembling Bike-chan appears in the anime; it is dropped at Lain's feet by a young girl in Shibuya.