For "illogical" routes like LHR-ATH-DUB, ITA Matrix is unreliable with availability. I find google flights to also be unreliable except for point-to-point tickets or a simple longhaul plus shorthaul on all airlines.
However I can certainly find LHR-ATH-FCO (oneways or returns) available to book on Expedia. On the A3 website, you may need to use multi-city function, and even so they may not be bookable.
And to answer the question in the title, searching on ITA will give you a fare basis and rules even if that ends up not being bookable - and entering random dates for FCO to LHR route A3+ gives various fares from ROM to LON which have rules such as NO DIRECT FLIGHTS ALLOWED and STOPOVER IN ATHENS PERMITTED AT EUR 75.00, indicating that this is one of the fares the OP is looking for, not just a combination of two fares.