I think it would be more accurate to say he was a "lobbyist who was a Republican". Putting the adjective "Republican" in front of the noun "lobbyist" is misleading as it could be wrongly interpreted to mean "a lobbyist who exclusively lobbied Republicans". That wouldn't stop the MSM from poor editing, however.
LOL. He's a Republican. Deal with it. It doesn't say he lobbied Republicans exclusively. It accurately describes him as a Republican lobbyist.