Presenting Lorelai Gilmore - S2-E6
Continuity mistake: During the presenter's introductions at the start of the ball, there's a shot of Lorelai from behind while she's seated alone at the table and we see the glistening necklace around her neck, but in the following shot facing Lorelai as she turns her head toward her parents the necklace has vanished, then she gets up and as Lorelai walks toward Emily and Richard the necklace has reappeared. (00:31:25)
Presenting Lorelai Gilmore - S2-E6
Continuity mistake: When Lorelai calls Chris to tell him about Rory's debut, she writes his new number on a gum wrapper. The shot changes to Rory. When it cuts to Lorelai again, she is reading the number from a notebook.
Presenting Lorelai Gilmore - S2-E6
Continuity mistake: When Christopher comes to the house and they are all outside talking, there is no garage on the side of the house. Only gates. In later episodes there is a garage.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.