Multiple league icons in dock

After closing the app, either through the in-client "x" or ctrl+q, three icons remain in the dock and cannot be forced to quit in any way, since they don't even show up as a running process. In the picture, you can see I have quit league twice today. Restarting solves this problem, but I want a better fix.

Thank you for help on this, since I'm not one to shut down my computer often.