N. American lynx feed in large part on snowshoe hares, I would guess that Euro lynx would eat similar things over there. The problem with reintroducing a predator is that once they are established, it's very difficult to open a hunting season for them. You would have every know nothing protesting and convincing the ignorant public that it's just not right to kill the endangered lynx. Case in point over here is the wolf and grizzly bear. It took a crazy amount of time and legal battles to get the wolf back on the hunt list. Wyoming almost had a grizzly hunt this year but it got cancelled at the last minute.