So I've been having trouble quitting Lightroom CC 2015.5.1 meaning that the option is always greyed out and I always have to force quit it. I'm on a mac (details below). Here's what it looks like:
I know that when I'm processing something it will be greyed out usually until the process is over. But even when I'm just sitting in the Library with nothing going on, it still won't let me quit.
I would suggest you to first update Lightroom to the latest version 2015.7.
Once updated, try to quit Lightroom and see if it still freezes or not.