Red Light on the Wedding Night - S2-E3
Visible crew/equipment: When Lorelai is talking to Babette about her shower in front of Luke's there is an audio guy crouched down hiding behind her in two shots. You can see his headphones. (00:22:55)
Like Mother, Like Daughter - S2-E7
Visible crew/equipment: When the guidance counselor introduces herself to Rory during lunch she tells Rory to meet with her after lunch, and when she walks away camera equipment is visible at the bottom left corner of the screen. Then, at the end of the episode, when Lisa asks Rory if she can join her for lunch, the camera equipment is visible again before it moves. (00:06:00 - 00:43:15)
Like Mother, Like Daughter - S2-E7
Visible crew/equipment: After the Mrs. Backward baseball cap line Lorelai goes to leave. Luke says "and by the way" and there is a camera part showing in the top left corner. (00:42:15)
Visible crew/equipment: While Dean is watching the play rehearsal, when Tristan starts talking about the "first kiss" in the wideshots facing Dean, we can see the boom pole moving at the top right corner of the screen. The boom pole is not part of the student production. (00:33:30)
The Bracebridge Dinner - S2-E10
Visible crew/equipment: During Friday night dinner, when they're discussing Emily and Richard's travel plans and then Richard's mood, in the wideshots from behind Emily lighting equipment is visible at the left side of the screen. (00:07:00)
The Bracebridge Dinner - S2-E10
Visible crew/equipment: During The Bracebridge Dinner, the entire time Richard is talking, each time they cut to Lorelei there is a mic on the right side of the screen which goes on for about six shots.
The Bracebridge Dinner - S2-E10
Visible crew/equipment: Right as Lorelei thanks everyone for coming there is a piece of equipment showing in the top left corner.
Richard in Stars Hollow - S2-E12
Visible crew/equipment: After Lorelai and Rory hug, a cameraman can be seen in the mirror next to them. (00:28:45)
Richard in Stars Hollow - S2-E12
Visible crew/equipment: At one point during Lorelai's argument with Richard at the end of the episode, a boom mic is visible above Lorelai's head. (00:40:25)
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)
Visible crew/equipment: At the end, when Luke walks into his apartment and passes Jess to get to the closet, we can see the reflection of the camera operator's legs in the bathroom wall mirror. (00:40:35)
Dead Uncles and Vegetables - S2-E17
Visible crew/equipment: Rory interrupts Lorelai and Luke talking at his kitchen table and as Lorelai walks out of the room you can see the boom mic drop in the mirror over Rory's head. (00:19:45)
Back in the Saddle Again - S2-E18
Visible crew/equipment: When Rory and her classmates arrive at Richard and Emily's house Paris opens the door, and just as they reach the dining room, the two boom mics are visible at the top of the screen. Also note the huge crystal chandelier is conspicuously missing. (00:25:35)
Back in the Saddle Again - S2-E18
Visible crew/equipment: When Emily opens the door for Lorelai and Rory for Friday night dinner, they walk in and sit in the living room, then during their conversation we can see four T-marks taped to the floor behind Emily. (00:37:40)
Visible crew/equipment: When Luke brings over the box of brownies for Lorelai he walks in and the front door is closed, then as they both walk away we can see the reflection of the boom pole moving on the door's glass. (00:13:25)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.