Clickair flies directly DUB-BCN for around 90 Euro all in at your time. It is the new LCC launched by Iberia and also is the first LCC to use LHR
From Barcelona to Nice, there is also a very nice night train, although it requires a connection at the border.
NCE-FCO is 50 Euro all in on
www.blu-express.com, an Italian LCC
Flying through LHR with its insane taxes seems like a waste of time IMO