I'm a Kayak, Hear Me Roar - S7-E15
Continuity mistake: When Lorelai picks up Rory and they head off on a drive there is no rearview mirror on the Jeep's windshield, but when they run out of gas and start their walk, a rearview mirror suddenly appears.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.