Dear Emily and Richard - S3-E13
Visible crew/equipment: In the flashback, when Emily is calling out for Lorelai but there's no answer, Emily spots something on the table, and just as she walks toward the table the crew member wearing a white short sleeved shirt is visible at the doorway. (00:39:15)
Dear Emily and Richard - S3-E13
Visible crew/equipment: In the flashback, while Lorelai is being wheeled to the delivery room, when Emily argues that she had a right to drive her daughter to the hospital, the reflections of the camera operator and the camera are visible on the glass beside Emily. Then it's seen again on the left glass window of the delivery room as it closes. (00:33:05)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.