Today, the FCO airport is closed through 1400 hrs / 2 pm local time.; the main highway to Rome was closed to non-emergency vehicles.
It's early to see how the authorities will be able to cope. The T-3 damage appears extensive, but we'll have to see how this plays out. In particular, some flights are arriving and departing other FCO terminals just now.
If I were flying to / from FCO, I'd stay in touch with the airline (and if it's practical, think about changing airports, at least in the short run).
Departure lounge is possibly not a major concern at FCO at this time; presumably airlines will be able to make temporary arrangements, but now they're likely dealing with ticket counter, check-in, baggage processing, gates etc.
I'm hoping others will weigh in as they experience the new interim ops at LIRF / FCO.
Link to BBC
In part: The airport was closed throughout the morning, with all outgoing flights cancelled and all but a few overnight long-distance incoming flights blocked.
Airport authorities said they hoped normal service would resume by midday on Thursday, but outward flights were still being cancelled mid-afternoon.
Many passengers were sent to the airport's three other terminals where they were subjected to long delays.
Airlines including national carrier Alitalia are offering alternative flights or refunds to affected passengers.
British Airways, which uses the terminal, had to cancel eight flights from London Heathrow to Rome and another was diverted to Naples.
BE SURE to look at this thread in the Italy Forum: Fire in Rome FCO / Fiumicino airport terminal 3 (May 2015).
This thread is mainly about disruptions to AA - US Flyers and those connecting to AA - US to some extent, so be sure to consult the above thread for more general issues, such as the threatened strike by airport workers alleging they are forced to work under hazardous conditions due to the fire.
Link to FlightAware AA cancelled flights.
Link to FlightAware US cancelled flights
Link to FlightAware LIRF / FCO flights information