Lain is visibly uncomfortable with her family and interacts awkwardly with every member, showing the extent of her isolation. If anything, all their family interactions - even the ones not involving Lain - seem forced from the very beginning. This foreshadows that her family is not, in fact, real. This is revealed in Layer 10. Even so, her "father" Yasuo still expresses affection towards her.
The only other family shown in the anime is the Masatsugu household, consisting of Shoko and her son Sho. They appear to get along well, even sharing a common interest in video games, but the family comes to an untimely end in Layer 10 when the Knights are exposed and Shoko dies.
In general, Serial Experiments Lain subverts the idea of family as a source of safety and stability. This contributes to the idea that reality is unreliable and that connections between people are fragile.