Factual error: This episode takes place in Connecticut in February. When Luke and Lorelei are leaving her house to go to the Vineyard, they are not wearing coats, there is no snow, and all the trees have leaves and plants are in bloom.
Continuity mistake: When Lorelai and Luke are talking in bed she is wearing a robe. It goes from on to off her shoulder with each shot.
Continuity mistake: When Lorelai enters the kitchen and sees Rory cooking the juicer is visible, but in the next shot you see Rory go to the drawer and get it. (00:25:24)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.