The Prodigal Daughter Returns - S6-E9
Visible crew/equipment: When Rory returns home Lorelai rushes out and they hug, then as the steadycam operator circles them the camera casts a moving shadow on Lorelai and Rory. (00:41:55)
The Prodigal Daughter Returns - S6-E9
Visible crew/equipment: Right after the opening sequence, in the shot of Emily reading the newspaper at the table, the T-mark is visible on the floor beside the door. (00:04:50)
The Prodigal Daughter Returns - S6-E9
Continuity mistake: April is in the diner taking a hair sample from Luke and takes his photo. She puts the camera in her pocket and in the next shot she has the camera in her hand again.
The Prodigal Daughter Returns - S6-E9
Continuity mistake: At the beginning of the episode, Lorelai can't get in the front door because Luke has installed a chain lock. Near the end of the episode, when Rory returns home and Lorelai rushes out the front door, there is no chain lock present on the door.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.