Sadie, Sadie - S2-E1
Continuity mistake: At the diner, when Lorelai stands at the counter telling Luke about Max's proposal, in the shots facing Lorelai we see the red ketchup bottle on the table behind her is either standing upright or lying on its side, changing a few times. (00:07:05)
Sadie, Sadie - S2-E1
Continuity mistake: When Richard enters to announce Rory being in the top 3% in her class his handkerchief is shown with 1 point. When he then walks to pour a drink and turns around, it has 2 points showing.
Sadie, Sadie - S2-E1
Continuity mistake: When Lorelai and Rory get home from the upsetting dinner from Richard attacking Dean, while sitting at the table one shot shows the Twinkies arranged on the plate in front of Rory on the table. In a few other shots, you see a few twinkies missing and not arranged.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.