LH have a link with Italy through AirDolmoti (I think thats how it is spelt!
). BA don't.
However, expanding in Rome maybe a good option whether they have links or not. Let Air One/easyJet/Lufthansa fight it out at MXP and take out Air One in FCO!
It would be a great idea but BA won't venture out of London in the UK, so I doubt we will ever see them venture to Europe (properly)