Other mistake: When Lorelai asks her mother which veil she should choose for her upcoming wedding to Max, Emily responds that her head is too big for a veil, and she could consider a tiara. When Lorelai responds quizzically with 'umm a tiara?' Emily says 'that's what I wore'. However, in s1e8, the photo album Rory looks through with her Grandparents features a picture of Emily and Richard that Emily calls their 'wedding photo' (in which she is pictured wearing a veil, not a tiara). (00:43:15)
Richard in Stars Hollow - S2-E12
Other mistake: Paris was looking to find the seedy side of Stars Hollow. Inside of Luke's she hid behind a menu commenting that she wanted to blend in. She then asked Luke if he gets a lot of truckers. We have all seen the exterior of Luke's and the town square. Paris has walked through it. Where, would a big rig possibly fit or park? Paris is extremely intelligent. She would not have asked the question. Doing so was totally out of character.
Presenting Lorelai Gilmore - S2-E6
Other mistake: Dean leaves the house the night before the debutante ball. He says goodbye and leaves the room but he never leaves the house. He never is seen going into the foyer and the door doesn't close.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.