Continuity mistake: Lorelai and Sookie take some containers out of the car and head towards Emily and Richard's door. When you see the next shot of them at the door, the containers Sookie is carrying are different from the ones she took out of the car, without her rearranging them.
Visible crew/equipment: When Emily tells Jason that she needs his guest list for the launch party, in the shots facing Emily and Richard we can see lighting equipment at the left side of the screen. (00:28:20)
Continuity mistake: While Lorelai and Sookie are with Emily doing the test meal, when Emily tells Lorelai to remove the plates she picks up the two plates and walks out of the dining room, but in the next shot the plates have switched hands. (00:23:35)
Visible crew/equipment: When Lorelai gets off the phone with her mother Rory walks into the house complaining about her roommates, and the boom mic dips into view at the top of the screen. (00:16:40)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.