I flew back from Rome on British Airways, who used a 767 on the Tuesday after Easter Monday to accommodate the crowd. BA operates its own lounge at FCO. Located after Security and Immigration, look for this sign to find it:
Go up one floor and the lounge is right in front of you.
The area is huge, easily one of the largest lounges in Europe (excluding London of course). Broken in to several seating areas, all using the standard BA lounge furniture:
The code for the WiFi is displayed on a PC screen towards the back of the lounge. There are two coffee/drinks areas and a separate food area. There were croissant, pastries and some crisps out when I was there just before lunch.
There were good views of the planes from the lounge.
The lounge is located some distance from the BA gates, a journey involving a three minute train ride, so it’s wise leave a little extra time. At the gate there was a separate queue for Fast Track passengers.