RORY: It’s okay not to like Jess.
LANE: I said I was happy for you.
Rory has that awkward conversation with her best friend where she gently lets Lane know that she knows she doesn’t approve of Jess, and that’s okay. She doesn’t need to pretend. Lane immediately feels bad about not liking Jess, but says that she’s protective of Rory, and doesn’t want her to be hurt.
Rory asks her to give Jess a second chance (even though she just said it was okay for Lane not to like him), and Lane gamely says that maybe they can double date with she and Dave some time. Double dating seems to be the default position on Gilmore Girls!
We never see if the two couples ever did go out together, but I imagine Jess would have refused – even though he would have a lot in common with Lane and Dave. It seems like a missed opportunity.
The Annotated Gilmore Girls 