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.
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: When Lorelai and Rory are in the kitchen talking about the to-do list, the camera is visible in the reflection on the microwave. You can see the cameraman's hand rotating the control to move the camera as Lorelai sits down. (00:07:20)
Richard in Stars Hollow - S2-E12
Visible crew/equipment: Lorelai is telling Rory there is no school - as it scans past the kitchen for a quick second you can see the top of the set.
It Should've Been Lorelai - S2-E14
Visible crew/equipment: After Sherry asks Lorelai where Rory is, she then asks Lorelai about her dinner with Christopher, and a mic drops into shot above Sherry's head. (00:38:05)
How Many Kropogs to Cape Cod? - S5-E20
Visible crew/equipment: When Emily notices her sewing box is missing and picks up the replacement there is a mic in the top right corner. (00:34:35)
Visible crew/equipment: When Taylor is complaining to Luke, Rory and Lorelai about faded paint, a bright green mic dips above Luke's head. (00:04:35)
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: A mic drops into shot just as Jackson accepts Sookie asking him on a date. (00:38:45)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: As Lorelei climbs into bed with Rory at 4:03 there is what appears to an open book being lowered out of the shot by a presumed crew member.
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)
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)
Visible crew/equipment: As Richard and Mitchum have their heated discussion in the bathroom, there is a mic seen through the whole scene in the top right corner that moves as the camera moves.
Visible crew/equipment: When Loralie walks out of the kitchen with a bowl of popcorn you can see the camera is slightly covered on the left side of the screen. (00:49:53)
Welcome to the Dollhouse - S6-E6
Visible crew/equipment: When Lorelei calls Taylor and she's on the bed with Paul you can hear someone from the crew snap at the dog to get his attention.
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.