The Fundamental Things Apply - S4-E5
Continuity mistake: Lorelai is in Luke's Diner talking to Luke. Lorelai is wearing a red sweater vest over a white blouse. When Luke is behind the counter, every time the camera faces Lorelai, the left side of her blouse goes from being tucked in under the vest (as if the vest were hastily put on), to being untucked (as it should be) quite a few times.
The Fundamental Things Apply - S4-E5
Continuity mistake: While Lorelai and Michel are at the diner Luke tells Lorelai to take Michel elsewhere, and when Luke goes behind the counter his shirt is perfectly dry in this wideshot and following closeup. but in the next wideshot, as Lorelai tries to get Luke's attention, we now see a round wet spot on Luke's back, but the problem is Lorelai has not yet tossed the lemon wedge at Luke's back that causes the wet spot on his shirt. Lorelai tosses the lemon wedge about ten shots later. (00:07:25)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.