Visible crew/equipment: At the start of the episode Rory and Lorelai are about to open the garage door. You can see a crew member in the reflection of the glass moving his arms around the camera - you can also slightly see his head for a split second. (00:39:00)
The Big One - S3-E16
Visible crew/equipment: At Chilton, after the teacher returns the graded papers to the students, when she walks to the front of the class her T-mark is visible on the floor. (00:04:55)
Eight O'Clock at the Oasis - S3-E5
Visible crew/equipment: When Emily gives Lorelai and Rory their drinks she mentions the cheese and walks away, then when Lorelai sits on the sofa the green tape marks are visible on the floor, where Emily had been standing by the bar. (00:40:20)
Haunted Leg - S3-E2
Visible crew/equipment: After Emily tells the new maid it would wonderful to remember the difference between the bells, as Emily, Lorelai, and Rory walk away from the front door, the white, red, yellow, and green tape marks are visible on the floor behind them. (00:32:00)
Haunted Leg - S3-E2
Visible crew/equipment: When the new maid tells Emily the dinner is ready even though it's only 6:30, Emily concedes and they all head to the dining room, and just as Emily says they all can be in bed by 9:00, we can see the boom pole and mic in the living room behind them, at the top of the screen. (00:33:20)
Visible crew/equipment: When Jess shows up at Principal Merton's office because he couldn't get prom tickets, as Jess shuts the office door the hand of a crew member is visible between the door and frame, slowing the moving door. (00:14:30)
They Shoot Gilmores, Don't They? - S3-E7
Visible crew/equipment: Before the dance marathon, when Lorelai and Rory are headed over to the first aid station they meet up with Sookie, and when Lorelai and Sookie cross the street we can see the T-marks taped to the sidewalk. (00:15:15)
Visible crew/equipment: When Richard walks into the dining room with the treat for the masses and serves Rory this special dish, we can see the boom mic bobbing about in the reflection on the window, at the left side of the screen. (00:00:15)
Visible crew/equipment: When Lorelai and Rory walk into the living room while Emily is on the telephone with her lawyer, the filming equipment is visible at the right side of the screen. Then when Emily walks over to the bar to pour a drink, the T-mark (looks like chalk) is a bit visible on the floor where she stands. (00:00:25)
Visible crew/equipment: After Luke catches Rory and Jess together Rory rushes out, and while Luke is lying down all the ground rules for Jess, the T-mark is visible on the floor near the door. (00:16:15)
Haunted Leg - S3-E2
Visible crew/equipment: After Lorelai and Rory meet Emily's new maid, when they walk into the living room the T-mark is visible on the floor where Emily stands. (00:32:05)
Those Are Strings, Pinocchio - S3-E22
Visible crew/equipment: When Lorelai, Sookie, and Jackson are "celebrating" they all sit down at the table, and we can see the T-mark on the floor behind Jackson. (00:11:30)
Say Goodnight, Gracie - S3-E20
Visible crew/equipment: When Luke gets home Jess confronts him about seeing his father, then just as Jess walks behind Luke the two T-marks are visible on the floor. (00:38:15)
Say Goodnight, Gracie - S3-E20
Visible crew/equipment: After Lane apologizes to Mrs. Kim in the kitchen, when Lane walks to the stairs as the doorbell rings, the reflection of the boom operator holding the boom pole is visible on the glass. (00:29:45)
A Tale of Poes and Fire - S3-E17
Visible crew/equipment: When Lorelai has the house-guests due to the inn's fire, Fred Jr. is sitting on the couch and calls her ma'am, then as Lorelai tells the boy to stop because it makes her feel old, the boom mic dips into view at the top of the screen. (00:27:30)
Visible crew/equipment: After dinner with Emily, when it cuts to Lorelai and Rory rushing into their house, an equipment pole is visible at the right side of the screen at the start of the shot, and a standing spotlight lamp is reflected in the wall mirror. Then as Lorelai walks back down the stairs the camera is visible at the left side of the screen, and when Lorelai exits, the spotlight lamp's reflection is visible again. (00:06:25)
Visible crew/equipment: When Lorelai returns from her trip she tells Rory that she needs food, and as they walk away from the car, we can see the reflections of the camera operator, camera, and boom mic moving on the surface of the car. (00:38:30)
Visible crew/equipment: While Dave, Brian, and Zack are in the car, when Mrs. Kim is speaking to Dave the reflection of the boom pole is visible in the window behind Mrs. Kim, then after she leaves when the car starts moving, the reflection of the reflector screen is also visible in Brian's window. (00:31:15)
Visible crew/equipment: During the Friday night dinner, something that looks like a microphone swings back and forth next to Richard's arm. It is most visible in the first shot of him (from behind).
Eight O'Clock at the Oasis - S3-E5
Visible crew/equipment: When Lorelai's date arrives she and Rory head downstairs, and as Lorelai tells Rory to phone with a fever if the date is a bust, the boom mic is visible in the foyer at the top of the screen. (00:25:30)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.