Luke Can See Her Face - S4-E20
Visible crew/equipment: After Luke invites Lorelai to the wedding, when she opens the car door the reflection of the camera operator (short hair) is visible in the wing mirror. (00:42:20)
Luke Can See Her Face - S4-E20
Visible crew/equipment: When Paris and Rory are at the hospital talking about Asher, Rory suggests getting something to drink so they both walk away from Asher's room, and just as Paris says, "Vanilla, it's a very old flavor," their yellow tape mark is visible on floor at the bottom right corner of the screen, which is where they were standing. (00:27:35)
Luke Can See Her Face - S4-E20
Visible crew/equipment: While Luke is looking around the inn's kitchen, Sookie introduces Lorelai to Shel Sausman, and we can see the white T-mark taped to the floor, at the bottom right corner of the screen. (00:07:00)
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.
Ballrooms and Biscotti - S4-E1
Visible crew/equipment: A mic drops into shot while Lorelai and Luke talk about luggage and the cruise. (00:34:30)
Visible crew/equipment: When Lorelai is in the diner questioning Luke about Nicole, during their conversation the reflection of the boom operator holding both arms up is visible on the window. (00:21:40)
Visible crew/equipment: When Lorelai is doing her baby-talk with "wittle Michel" he continues walking as she stops in front of Luke's, and the reflections of the camera operator and camera are visible on the glass door. (00:16:10)
Visible crew/equipment: When Emily tells Jason that she needs his guest list for the launch party, in the shots facing Emily and Richard we can see lighting equipment at the left side of the screen. (00:28:20)
Visible crew/equipment: When Lorelai gets off the phone with her mother Rory walks into the house complaining about her roommates, and the boom mic dips into view at the top of the screen. (00:16:40)
Ballrooms and Biscotti - S4-E1
Visible crew/equipment: When Sookie takes Lorelai out to the shed because Jackson doesn't want to know the sex of the baby, just as Sookie opens up the doors, we can see the hand of a crew member at the lower right side of the screen, stopping the moving door. (00:12:20)
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.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.