Eight O'Clock at the Oasis - S3-E5
Visible crew/equipment: When Lorelai is on the phone trying to get the name of the guy who she met at the auction, she mentions the winning lottery ticket, and as Lorelai sits down at the table the filming equipment is visible at the right side of the screen. (00:16:20)
Eight O'Clock at the Oasis - S3-E5
Visible crew/equipment: When Lorelai's date arrives she and Rory head downstairs, and as Lorelai tells Rory to phone with a fever if the date is a bust, the boom mic is visible in the foyer at the top of the screen. (00:25:30)
Eight O'Clock at the Oasis - S3-E5
Visible crew/equipment: When Emily gives Lorelai and Rory their drinks she mentions the cheese and walks away, then when Lorelai sits on the sofa the green tape marks are visible on the floor, where Emily had been standing by the bar. (00:40:20)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.