It Should've Been Lorelai - S2-E14
Visible crew/equipment: After Sherry asks Lorelai where Rory is, she then asks Lorelai about her dinner with Christopher, and a mic drops into shot above Sherry's head. (00:38:05)
It Should've Been Lorelai - S2-E14
Continuity mistake: While Lorelai and Christopher are talking at the table at Luke's, a blue coffee mug appears only in one shot but not the rest of the scene.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.