Rec'd this reply this morning - Alitalia seems to be not on their list. Interesting they list several Skyteam airlines but not Alitalia.
So yes, I'd say definitely worth contacting them (and perhaps Alitalia as well) on this.
Please be informed our Lounge accepts passengers from: Finnair, Virgin Atlantic, Etihad, China Airlines, KLM, Delta, Air France, Kuwait, Biman and Vistara (only by invitation) , Tap Portugal, LOT, Turkish Airlines (only by invitation)