Rien. I always book my Delta connection on the same ticket when I fly LP in and out of JFK, and sometimes when I arrive from T4 to T1, they don't even know that I'm in connection at JFK (my bags do get automatically checked through, so I do not have to claim and recheck at JFK which is nice - but the bags are not tagged as LP). And on the return, they ask if I know how to get to the AirTrain and then leave me. It would be SO COOL if they offered a tarmac transfer between T1 and T4 - this feels feasible. It is nice to have access to D1 check-in, security, and lounge when flying home. I also am curious to see what the LP ground experience will be like at the new T1.