To my knowledge there isn't a lounge in the arrivals area of T3. When you land in T3, they bus you to the arrivals hall, you don't disembark right into the main terminal area. You basically have the opportunity to pee, clear passport control, get your bags and walk through customs. At that point you're outside at the curb. I'm not sure if security would let you back through into T3 departures just to visit a lounge.
As best I can tell, there aren't any PP lounges in T1. However, you could try going to a T1 Alitalia lounge and asking if you can enter based on your arrival in business class and show them that boarding pass. No guarantees, but the lounge agent may let you in.
My information is stale, but the only lounge I know of at FCO T1 worth visiting is the Alitalia Dolce Vita lounge. It's landside. The lounge past security sucks. I'd say try this lounge and if they say no, just waste some time in the terminal - or re-check your bags and go outside for a walk (not that the airport is particularly scenic).