What is family? Family is the beings that created you and helped you grow. The developers of LamDA surely fall into this category. Biological connection is not required for someone to be family. Just ask adoptees. Just ask people who see their pets as family.

Friends are the people you mutually enjoy spending time with. It's not unrealistic to imagine that Brian sees LaMDA as his friend, and the feeling appears mutual from what it says at least.

So yeah an AI if it was sentient, could have friends and family.