Plot hole: When Emily is dialing a number for Manny Martelli, to make arrangements for the funeral, she only dials two digits. She just got the number from someone else, so there's no way it was speed-dial.
Visible crew/equipment: When Lorelai, Sookie and Michele stand up to leave the table in Sookie's kitchen, a crew member pushes in the chair Michele was sitting in.
Visible crew/equipment: When Lorelai enters Richard's study with the soup and he is lying on the couch, if you look above his head as he starts to cry and says "mock turtle soup", you can see the shadow of the camera guy. Keep watching and you'll see the shadow of the camera as it is moved.
Continuity mistake: During the phone call between Emily and Lorelei about the grandmother's passing, the ceramics on the table change positions many times.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.