Eight O'Clock at the Oasis - S3-E5
Visible crew/equipment: When Lorelai is on the phone trying to get the name of the guy who she met at the auction, she mentions the winning lottery ticket, and as Lorelai sits down at the table the filming equipment is visible at the right side of the screen. (00:16:20)
Those Lazy-Hazy-Crazy Days - S3-E1
Visible crew/equipment: When Lorelai and Rory are on their way to the festival they stop at Sookie and Jackson's house, and as they approach the front door, the reflections of the camera operator and camera are visible on the door's window. (00:25:05)
Visible crew/equipment: While Lorelai and Rory are making a list of everything Luke needs to fix, after Lorelai mentions Dick Van Dyke, the reflections of the camera and a crew member are visible on the left glass door of the corner book cabinet. (00:07:55)
Visible crew/equipment: During the family dinner at the inn Trix is seated beside Richard, and when Trix tells Lorelai, "He's a go-getter your father, not completely dissimilar to yourself," in this shot facing Trix and Lorelai the boom mic quickly dips into view at the top of the screen, and what looks like a bit of filming equipment is also visible at the bottom right corner of the screen. (00:37:40)
Visible crew/equipment: When Lorelai and Rory are finished preparing their house for Gran's visit, just as Lorelai and Rory are walking towards the door we can see a T-mark and other tape marks on the floor. Then after showing Gran the house, when they're leaving a rug has appeared covering all those tape marks. (00:30:15)
Visible crew/equipment: When Trix shows up unannounced Emily confides in Lorelai that she's unprepared, and just as Emily and Lorelai exit the foyer two taped T-marks are visible on the rug behind them, at the bottom of the screen. (00:19:50)
They Shoot Gilmores, Don't They? - S3-E7
Visible crew/equipment: After Luke fixes Lorelai's broken heel it cuts to Lane at the first-aid/rest stop at Miss Patty's, and when Lane walks toward her table, we can see the T-marks taped to the floor. (00:35:10)
Visible crew/equipment: After Luke tells Lorelai that Jess is gone, when Luke tells her that he failed Jess, the reflections of a crew member and the camera are visible on the window behind Lorelai. (00:07:20)
Visible crew/equipment: After Lorelai gets off the phone with Richard, when it cuts to the bakery we can see the reflection of the camera as it moves past the chrome display case. (00:11:50)
Visible crew/equipment: When Rory (holding the muffins) and Lane are walking on the porch heading to the garage, the reflections of crew, equipment, and the camera operator are visible on the windows. (00:11:05)
Visible crew/equipment: While Rory and Paris are in Charleston's office, when the two girls are arguing the shadow of the boom mic is moving around on the wall behind Rory. (00:23:10)
Dear Emily and Richard - S3-E13
Visible crew/equipment: In the flashback, when Emily is calling out for Lorelai but there's no answer, Emily spots something on the table, and just as she walks toward the table the crew member wearing a white short sleeved shirt is visible at the doorway. (00:39:15)
Dear Emily and Richard - S3-E13
Visible crew/equipment: In the flashback, while Lorelai is being wheeled to the delivery room, when Emily argues that she had a right to drive her daughter to the hospital, the reflections of the camera operator and the camera are visible on the glass beside Emily. Then it's seen again on the left glass window of the delivery room as it closes. (00:33:05)
Visible crew/equipment: When Rory and Paris are waiting to see the Headmaster, each time the door to Charleston's office is opened, the actor's T-mark is visible on the floor in the doorway. (00:22:25)
Visible crew/equipment: While Rory and Lane are in the beauty supply store, when they both crouch down looking at the lower shelf, the T-mark is visible behind Lane where Rory had been standing when they first walked in. (00:12:00)
Visible crew/equipment: When Luke gets frustrated with the construction noise he storms out of the diner, and at the start of the next shot we can see an actor's T-mark taped to the ground at the bottom of the screen, where Luke will be standing in a moment. (00:03:40)
One's Got Class and the Other One Dyes - S3-E4
Visible crew/equipment: Right before Lane walks out of band practice you can see part of the mic guy's body and elbow at the right side.
The Big One - S3-E16
Visible crew/equipment: When Lorelai and Rory are at Richard's while Emily is away visiting her friends, Richard steps out to answer a call. When Richard returns we can see a blue T-mark taped to the floor behind Rory's side of the sofa. This T-mark is visible again when Richard asks about Rory's speech, because he'd like to be there. (00:20:00)
One's Got Class and the Other One Dyes - S3-E4
Visible crew/equipment: Right before Lane walks out there is a crew member watching the scene from the doorway of the back room and then she quickly ducks back inside.
Haunted Leg - S3-E2
Visible crew/equipment: Rory gets dragged in the bathroom to discuss hem lines and the entire time the mic guy can be seen in the shadow on the wall behind her.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.