Last night and today Lightroom 6 has not been working. I am using Mac OS X Yosemite. After the splash page, the grid opens and I can select one or two files to export. After that nothing works. The mouse pad works, but no amount of clicking will generate a response. I have to close and force quit. If I try to reopen and Import anything, Lightroom 6 just stops completely and I have to force quit again. I see others in the forum are having the same kind problem and not having much success with getting an answer from technical support.
Try turning off the "Add photos screen" in Preferences->General. Also turn off the graphics card acceleration. If neither works, try rolingl back to LR 6.1.1. There are lots of freezing bugs in 6.2.1 on Mac OS X that make it unusable for some people. Instructions here: http://www.lightroomqueen.com/how-do-i-roll-back-to-lightroom-2015-1-1-or-lightroom-6-1-1/