What version are you running? To find out go to:
Help >> System Info
I think Mac OS 10.9 can only be updated to 2015.1 or 2015.1.1
If you wish to start over you will need to uninstall and then re-install.
Launch Finder and go to Applications >> Utilities >> Adobe Installers
Uninstall Adobe Lightroom
Re-boot your mac, and then go to the link below to download LR6
After installation you can download the update patch applicable to your OS, but start with the main download (727 mb for Mac).
I have Lightroom 2015.8.
For the type of slow performance problem I described, does reinstalling LR typically help it perform better?
I'm surprised you were able to install the 2015.8 update on your system? Are you sure you have OSX 10.9?
Yes, I have LR 2015.8 on two computers running os x 10.9.5.
Only the older computer, the MacPro 2009 has trouble with slow LR.
It could be some incompatibility issue. If you look at the system requirements at the link I posted it states macOS 10.12, 10.11, or 10.10
It's really up to you to decide if you wish to roll-back to the earlier features.