They Shoot Gilmores, Don't They? - S3-E7
Continuity mistake: When Luke fixes Lorelai's shoe, he squeezes glue onto the broken heel and places the glue bottle down on the seat to his left, then he holds the heel to the shoe with both hands, but in the next shot that glue bottle is suddenly back in Luke's hand while he's still holding the heel to the shoe. (00:34:20)
They Shoot Gilmores, Don't They? - S3-E7
Continuity mistake: During the dance marathon while Luke is fixing Lorelai's shoe, Taylor can be seen on the podium in the background changing from standing to sleeping over and over.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.