Well, now that is quite curious....Your issue is 100% cpu and lag, yet what you are posting here doesn't show up that issue. Game taking 60-90% is normal, and shouldn't cause an issue lagging there....
So it sounds like homework time again for you...If you have dual monitors it will make the next step easier...
Play the game and keep Process Explorer running and get the game to start lagging and stuttering, then look at Process Explorer and see how much use DAI has, and if there is another process running.
System Idle is just a phantom catagory basically saying how much free power your CPU has, it isn't anything to worry about.
System would be an issue...
Or like I posted before, anything taking 5% or more when trying to play can be an issue.
Because simple logic dictates if the game is using only 60-90% of your cpu, then it isn't the sole cause of your cpu maxing out, so you now need to find what is maxing it..
So put Process explorer up, click on the cpu tab, so it lists your usage from greatest to least, make sure you have the slider all the way to the top and get it to act up and lets see what is causing your issue...