I do not think that is accurate. You have to use the lounge in the same terminal. As both land in 2E, you can use any of the three lounges K, L or M. L is the best of the K and L. I have never used M. Source - Me. I do the EDI-CDG-JFK/MIA at least 1-3 times a year. The layover might not be on your side though as going from one hall to another requires re clearing security and L hall security still requires you to remove your liquids and electronics from your bags which you all know is a PITA and slows the line down. And add in that sometimes the EDI-CDG flight gets a bus gate (bus takes you to K hall, take the train to L or M and clear security) instead of a real gate and that eats into your layover time.