With that version of OS X the latest version of LR you can use is CC 2015.6.1/6.6.1.
** Lightroom CC 2015.1/Lightroom 6.1 and earlier versions are supported on Mac OS X v10.8. Lightroom CC 2015.6.1/Lightroom 6.6.1 and earlier are supported on Mac OS X v10.9. Lightroom CC 2015.6.12/Lightroom 6.12 and earlier are supported on Mac OS X v10.10.
So you either have to downgrade LR by uninstalling then go to this link,
Download Photoshop Lightroom
And download the Base Installer and the 6.6.1/2015.6.1 update.
Then Never check for updates again.
Or upgrade OS X to 10.11.x or above.