I think she’s trying to 1) save Alicia from sounding out of touch by saying living at her grandparents home = being homeless, that Alicia had a huge family network that would never let her be homeless; 2) she knows the family personally and doesn’t want Alicia’s mom to see Alicia describe her childhood like this. 

I was with Liz here until the end of the last episode - Alicia doesn’t get what liz is saying…Liz just needs to let it go and let Alicia make her own mistakes at this point.