The Lounge I Mosaici is nothing to write home about. Free booze including prosecco and something to nibble (usually the offerings disappear very fast). I have only used this lounge when flying AY business class or using Diners Club Card. However, I have been able to use some of the AY contracted lounges not shared by BA by showing my Gold (or Silver) Executive Club Card. In one thread I suggested that we would share which AY (and other OW) out-sourced lounges accept BA cards. I usually use the check-in desks to enquire the rules in order to avoid the possible embarrassment of being denied but this is a matter of personal preferences.

AFAIK the BA lounge at Fiumicino is beyond the Schengen border, so it might not be the best solution for your FCO-HEL flight operated by AY.