Forgiveness and Stuff - S1-E10
Visible crew/equipment: When Lorelai and Dean are talking through Rory's open window, Lorelai tells Dean that they have a nice front door he might want to use, and when Dean walks away the moving boom pole is visible through the top of the glass window, in front of the lattice. (00:13:35)
Forgiveness and Stuff - S1-E10
Visible crew/equipment: After Richard is brought to his hospital room, when Luke tells Lorelai that she's avoiding seeing her father, the boom mic dips into view at the top pf the screen when she says, "You know what hurts? A screwdriver in your head." (00:30:25)
Forgiveness and Stuff - S1-E10
Continuity mistake: When Miss Patty finds Rory and Dean asleep, they are asleep face to face. In a subsequent shot they are lying on their sides, Dean behind her.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.