Visible crew/equipment: During the family dinner at the inn Trix is seated beside Richard, and when Trix tells Lorelai, "He's a go-getter your father, not completely dissimilar to yourself," in this shot facing Trix and Lorelai the boom mic quickly dips into view at the top of the screen, and what looks like a bit of filming equipment is also visible at the bottom right corner of the screen. (00:37:40)
Visible crew/equipment: When Lorelai and Rory are finished preparing their house for Gran's visit, just as Lorelai and Rory are walking towards the door we can see a T-mark and other tape marks on the floor. Then after showing Gran the house, when they're leaving a rug has appeared covering all those tape marks. (00:30:15)
Visible crew/equipment: When Trix shows up unannounced Emily confides in Lorelai that she's unprepared, and just as Emily and Lorelai exit the foyer two taped T-marks are visible on the rug behind them, at the bottom of the screen. (00:19:50)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.