So far, Lizzie does not follow Fitz and Gigi on twitter. While I find this nonsensical, as she’s friends with them, it does mean she doesn’t see their conversations about her. So that makes sense.
Darcy, however, follows both Fitz and Gigi. I tend to think the D doesn’t use twitter that often, but. He definitely can see the conversations that his BFF and little sister have about him.
Which is endlessly amusing to me.