You may try few steps to fix this issue.
1. Reset Lightroom preferences back to default, refer: Preference file and other file locations | Lightroom CC and 6
2. Check if there's any .lock file saved to the same location of your Lightroom catalog, If yes then rename the file to .lock.old
Thank you kindly for your speedy response.
I tried #1 and the Reset Preferences window never appear. LR icon just bounced up and down in dock and I had to Force Quit.
I tried number #2 and found "Lightroom Catalog.lrcat.lock", I changed to "Lightroom Catalog.lrcat.lock.old". Tried opening LR and again, the icon just bounced in the dock with me having to Force Quit.
Please uninstall Lightroom, restart your machine and reinstall it.
Download link for Lightroom 6: http://trials3.adobe.com/AdobeProducts/LTRM/6/osx10/Lightroom_6_LS11.dmg?PID=2159997
For Updates: Download Photoshop Lightroom