The Lorelais' First Day at Chilton - S1-E2
Continuity mistake: When Lorelai drives Rory to Chilton, the license plate at the front of her Jeep goes from being attached to the center of the bumper, to the side of the bumper, then back to the center of the bumper. Additionally, the Jeep's rearview mirror has vanished when they're parked at Chilton. (00:03:25)
The Lorelais' First Day at Chilton - S1-E2
Continuity mistake: While Rory is at the administration office Miss James gives her the Chilton map, schedule, etc. Then just as Miss James tells Rory that Mr. Winters, the guidance counselor, handles everything except bulimia and pregnancy, Miss James is wearing eyeglasses in the shot facing Rory, but in the previous and following shots she is not. (00:15:50)
The Lorelais' First Day at Chilton - S1-E2
Continuity mistake: Luke uses a red screwdriver trying to get something out of the toaster and leaves the screwdriver in the toaster while he goes to get coffee. When it cuts back to Lorelai, the screwdriver is on the counter, beside the toaster. (00:18:20)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.