See in the BIOS if you can inactive it, and if there isnt any option, make it inactive in device manager ;p
Try switching , inactive / take you external graphic out and test with the motherboard's graphic.
You should check all the connections to the GPU and Motherboard and make sure that everything is connected properly. If you don't find anything that might be wrong you should try replacing the current GPU you have with another that you know for sure are working, this way you can check if the GPU is the problem or not.
I'm gonna try using my motherboards graphic card. (Using the motherboards graphic card had the same problem.)
Does the lag also happen when not playing a game? E.g. just browsing the web, not graphics-intensive stuff.
Have you already tracked the temperature of the card itself? Does the card get a lot hotter in laggy times? Does it make noise (fans?)?
Have you tried other resource-intensive games?
Its weird that it happens when your not doing something resource-intensive, but my guess would also be heat-related, the firmware could temporary stop the hardware and wait for it to cool down a bit before resuming, but its not an usual practice
Have you tried the usual suspects? (Virus, Malwares, etc..)
Did you try to use your onboard graphics card already? Do those huge lag spikes disappear then?
Maybe alittle late, but I would try a better PSU.
Use Afterburner to monitor GPU frequency while you're in a game, and see if it changes when your FPS drops