Hello,
I had the same problem with an BA Avios booking for a reward flight on JL.
BA does not have the option to enter the data for the flight and JL website did not find the booking.
I called JL hotline and the lady had no problem taking all the relevant data via the phone (passport and hotel details for US inbound flights).
She said it should be available during online check-in, but since I am not sure if this is enough time for the data to be entered before US flights, I preferred doing it via their hotline.
Hope this helps.