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)
Star-Crossed Lovers and Other Strangers - S1-E16
Visible crew/equipment: During Friday night dinner, after Emily suggests brandy in the living room Lorelai excuses herself, and when she stands up in the wideshot the boom operator is visible at the left side of the screen. (00:31:25)
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 Lorelai and Rory are trying to get to Luke's they wind up in the alley, and in the next shot inside Luke's we can see the reflection of the moving camera on the glass door, behind the guy wearing a blue check flannel vest. (00:11:50)
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: While Lorelai and Luke are in the diner's storeroom, just as Lorelai makes a comment about not knowing what's going on in Rachel's head because she's not a Vulcan, the boom mic dips into view over the white container on the top shelf, at the top right side of the screen. (00:30:00)
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)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.