The Bracebridge Dinner - S2-E10
Continuity mistake: When Rory is checking in Lane and Mrs Kim, twice in a row it shows her close her folder and hold it at her side and in the next shot it is still open.
Those Lazy-Hazy-Crazy Days - S3-E1
Continuity mistake: In the first shot you can see Rory's laptop open in the background, but when she walks over to her desk and sits down, it's closed. (00:02:15 - 00:04:45)
We Got Us a Pippi Virgin - S5-E5
Continuity mistake: When they are starting Pippi and Luke is asking about her hair, you can see Dean's hand on Rory's shoulder on the side of the shot. Then it pans to them and then Dean is putting his arm around Rory.
Continuity mistake: In this episode, when Logan goes to see Lorelai to ask her permission to propose to Rory, Lorelai asks Logan if he wants any french fries. They sit down and the to-go container is open, when the camera zooms in and then back out it's closed again.
Like Mother, Like Daughter - S2-E7
Continuity mistake: When Mr. Charleston is looking at Lorelei's parent file, he closes it and starts talking and in the next shot he is seen closing it again.
Rory's Birthday Parties - S1-E6
Continuity mistake: Rory's piece of birthday coffee cake changes sizes throughout the whole scene.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.