Bear suit
From Serial Experiments Lain wiki
Lain Iwakura's bear suit appears several times in the anime. It provides her with comfort when in intimidating situations, such as when using a NAVI for the first time in a long time. It also functions as Lain's pajamas.
Lain also has a bear hat that appears only in Layer 01 when she turns on her NAVI.
Although its screentime is very limited, the bear suit has left a powerful impact on the fandom and bear motifs can be seen in a lot of Lain fanart.
Meaning
Lain's pajamas are meant to shield her from the outside world. Every time she wants to talk to her family, she wears them.[1]
