Contract lounges usually have a huge book of all possible combinations for each airline they deal with. A few years back, the lounge attendant in Copenhagen had to do some digging to confirm that I was allowed in as an Air France customer with a JAL OWE card. (the lounge that prepademic at least was at the old BA lounge location forget the name now, very brightly coloured, but quite nice) It was all listed in the book, and accepted. To her credit, I was let in while she did her digging. But I guess not all will have the patience to look.

Also there was a posting on OMAAT that ITA status and Skypriority benefits are rather sketchy