There is nothing in the cloud - it's just the naming.
The application is installed and running locally. This is true for the CC version (LR CC 2015) and for the stand-alone version (LR 6). They are absolutely the same, except for the additional features that are unlocked if you have a CC subscription.
The issue must be something else. What type of graphic card do you use in this PC?
First, try and see if deactivating GPU acceleration helps: Adobe Photoshop Lightroom Help | Lightroom Graphics Processor Acceleration (GPU) Troubleshooting & FAQ
Thank you for joggling my memory!...Going through a Windows re-install and then re-installing every freaking application only a few days after I upgraded to CC2015 and then trying to get back on course and working ASAP has made it difficult to remember what I have done and not done and when. I had read to turn the card off soon after the upgrade and did on the initial install, but forgot totally about it when i did the re-install and it does made a huge difference.
I did think that even though the application is on my hard drive that maybe Lightroom might be communicating to the cloud all the time causing it to be less responsive. Going to Portraiture when exporting still gives a white screen and short delay as the app comes in, but I can live with that if all my basic Lightroom needs are back to normal. I love the program and only go into Photoshop when major retouch work is needed.