Mac client wont open

So today I decided I was going to get on league and do a little bit of ranked to get to silver so I could duo with my friend. But last night I had to leave due to a family emergency and had to shut down my mac with league still going. I hit the "Leave Game" button and then went to shut down my mac. So today I click on the League of Legends on the task bar but it says. Another instance of this is still running, terminate it? I hit ok and wait for it to pop up on my task bar. But it never does. Can someone please help me? I really want to play league today.