Not quite right... I was on LY27 to EWR, After landing i had 5 hours for my connection, Went to the checkin, showed my TPL Card, and got the invitation card to the lounge at the marriot... And i took a guest with me (that was flying ly28 back to israel the same day, but she was not even a TL)

As long as you pass thru EL-AL check-in and get the invitation they will let you in to the lounge, if you appear out of the blue in the lounge (if its a non EL-AL dedicated lounge), they wont let you in.

As for JFK/CDG, I have been into the lounge when flying with others as well (but that's not fair, They never asked to see my ticket! 8-))