Visible crew/equipment: After Sookie dumps her pan of ratatouille in the sink she suggests going to Cicero's, and just as Jackson says, "They have good ratatouille. OK, so long as I can keep my shoes on," the reflection of the dolly grip pulling the camera dolly is visible on the window. (00:38:20)
Introducing Lorelai Planetarium - S7-E8
Visible crew/equipment: While April is wrapping the gift for Sabrina, when Luke talks to her about the party, the reflections of the set's reflector screen and a crew member wearing blue pants are visible on the toaster's silver surface. (00:23:50)
Visible crew/equipment: When April shows up at the diner, we can see the reflection of the moving boom pole and mic at the top of the window, behind Luke. (00:14:00)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.