Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Rory shows up at Luke's to meet Lorelai, just as Lorelai says, "Nice face you got on there," we can see lighting equipment at the top left side of the screen. Then, when Luke brings them coffee it's visible in the shots from the same angle. (00:11:30)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: After Rory takes Tristan's invitation and walks away, when it cuts to Emily and Lorelai shopping at Damion's, just as Emily notices the hat we can see the crew member and equipment at the right side of the screen. Then, when Emily finds the light-up bracelets and shows Lorelai, some lighting equipment is visible at the left side of the screen and cables are on the floor behind them. (00:08:30)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: At Chilton, when Rory walks past the girls talking about another obligation party, in the next shot facing Rory we can see lighting equipment at the right side of the screen. (00:08:20)
Visible crew/equipment: While Rory is at Luke's doing her homework, when Lorelai walks in and is about to sit down at the table with Rory, the lighting equipment is visible at the right side of the screen. (00:19:50)
Visible crew/equipment: When Lorelai talks to Emily at the Independence Inn, a boom mic briefly drops into the shot. (00:21:25)
Visible crew/equipment: When Paris drops her book on the floor in English class, to jolt Rory out of her daydream stupor, a boom mic is visible above Liza Weil's head. (00:16:45)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: While Emily is instructing the servants before the party, when she tells one servant, "I want those six inches apart, get a ruler," there are two problems with this medium shot. First, lighting equipment is visible at the top right side of the screen over the lamp, and second, it's a flipped shot. Note the painting and lamp are reversed in the medium shot, compared to the next wideshot which is fine. (00:17:45)
Star-Crossed Lovers and Other Strangers - S1-E16
Visible crew/equipment: While Lorelai helps her daughter get ready Rory holds up the two sweaters on hangers, and in the shot facing Lorelai as she tells Rory not to clash with the decor, lighting equipment is visible at the right side of the screen. (00:17:50)
Double Date - S1-E12
Visible crew/equipment: While Lane is trying to chat with Todd during the Double Date, when she asks if he likes Fugazi he tells her it's his sister's T-shirt, and just as Lane answers, "Oh," the boom mic dips a bit into view over Lane, at the top of the screen. (00:23:10)
Visible crew/equipment: While Lorelai is cleaning out the fridge, when she picks up the book and asks Rory to give the book back to Max, lighting equipment is visible at the right side of the screen.
Forgiveness and Stuff - S1-E10
Visible crew/equipment: When Lorelai and Dean are talking through Rory's open window, Lorelai tells Dean that they have a nice front door he might want to use, and when Dean walks away the moving boom pole is visible through the top of the glass window, in front of the lattice. (00:13:35)
Visible crew/equipment: After Rory asks Lane if Rich still wears the Star Trek shirt, when it cuts to Sookie in the kitchen, we can see two T-marks taped to the floor behind her. (00:08:40)
Visible crew/equipment: In the last shot, when Rory starts telling Lorelai all about the market kiss with Dean, some lighting equipment becomes visible at the right side of the screen, as the camera pulls back. (00:43:20)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Emily raves about Sookie's hors d'oeuvres, the shadow of the boom mic is bobbing around at the top of the screen. (00:35:10)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Lorelai gets home while Rory is on the phone, just as Lorelai jokes about Justin and Britney, filming equipment is visible at the left side of the screen. (00:06:35)
Kill Me Now - S1-E3
Visible crew/equipment: When Lorelai and Emily have a private chat about Rory playing golf with Richard, Lorelai tells her, "You win," and as Emily walks out of the room, the lighting equipment is visible at the left side of the screen. (00:06:00)
Visible crew/equipment: At the Kim house, when Lane and Rory reach the kitchen doorway, just as Mrs. Kim tells Lane that she has "muffins with no dairy, no sugar, no wheat," the boom pole dips into view at the top right corner of the screen. (00:11:35)
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)
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)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.