Back in the Saddle Again - S2-E18
Visible crew/equipment: When Emily opens the door for Lorelai and Rory for Friday night dinner, they walk in and sit in the living room, then during their conversation we can see four T-marks taped to the floor behind Emily. (00:37:40)
Back in the Saddle Again - S2-E18
Continuity mistake: When Lorelai sits down with Dean to discuss how "clingy" he is with Rory, both Lorelai and Dean's hand positions change between shots, specifically whether their fingers are laced, resting normally on the table or raised in the air.
Back in the Saddle Again - S2-E18
Visible crew/equipment: When Rory and her classmates arrive at Richard and Emily's house Paris opens the door, and just as they reach the dining room, the two boom mics are visible at the top of the screen. Also note the huge crystal chandelier is conspicuously missing. (00:25:35)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.