Visible crew/equipment: When Rory gets the photo album from her mother's bedroom and shows her Grandparents, just as Emily reminds Richard about getting the baby dress in London, a piece of filming equipment is visible at the right side of the screen. (00:27:25)
Visible crew/equipment: While Lorelai and Max are kissing on the staircase, when Lane walks up and surprises them, the two tape marks are visible on the lower step. (00:34:15)
Visible crew/equipment: Lorelai and Max are at the bookstore watching the movie, and when it cuts to Rory picking up the slice of pizza, the lighting equipment is visible at the right side of the screen. (00:25:40)
Visible crew/equipment: After the cook tells Emily that she can't make it because of the storm, in the next few closeups of Emily the lighting equipment is visible beside her, at the right side of the screen. (00:18:45)
Visible crew/equipment: After Rory asks Lane if Rich still wears the Star Trek shirt, when it cuts to Sookie in the kitchen, we can see two T-marks taped to the floor behind her. (00:08:40)
Visible crew/equipment: Right before Max and Lorelai go up the stairs, a crew member's arm is seen on the right side as they step out of the shot. (00:34:00)
Visible crew/equipment: Near the end of the episode when Rory comes home and is standing on the porch talking to Lorelai at the door, right before Rory says "Hi" you can see a crew member in the background, standing in the bushes on the other side of Lorelai's jeep and then moving out of sight (toward the left side of the screen). (00:39:20)
Visible crew/equipment: When Rory is dropped off in the morning, he walks up the front porch, Lorelai greets her at the door. Behind Rory across the driveway in the bushes is a man. The many slowly hides back into the bushes. (00:39:19)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.