Considering I strongly dislike the english (and kinda the welsh) it's hard to get behind a team consisting mainly of them, and of course I wouldn't feel that anything with "british" in it's name would represent me.
Also people (media, commentary, ex-players and even current players) have a tendency to drop the Irish part and just say "The British Lions", which really grinds my gears.
All that I would care about is Irish lads making the team/scoring the tries, and not getting injuries. I wish them luck, but would be happy enough with them losing 3-0 (especially since Ireland beat NZ last November)
I wonder if I'd feel different if it was the Celtic and English Lions...