I'm almost certain that the freezing is the graphics hardware, though I don't know why this is suddenly happening: I've been using this machine since last October without issue. I am not using the trackpad - I am using a USB mouse. I have also notices that when music was playing when the freeze happened, this stuttered and went metallic sounding.
When I can actually hover over that steep peak, it reports that it is procexp64.exe - i.e. process explorer - now I know it's not that, because it happens when it's not running e.g. when using Chrome. So it can't be application-based, it must be drivers I think.
All I can think of is that there has been an update in Windows or elsewhere that is buggy, though I don't know how to roll back or where to roll back to. Rolling back seems to be a very crude way to pinpoint the issue.
The reason why I think it's the graphics is because, of the times it has frozen for a second or two, a few times out of those occasions, the screen has gone black, to come back with everything being redrawn and a message that "Display Driver Stopped Responding and Has Successfully Recovered" - speech bubble in bottom left of Desktop mode.
I may try a version of the following solutions:
http://www.computertipsfree.com/display-driver-stopped-responding-and-has-successfully-recovered-nvlddmkm-nvidia-atikmdag-ati-windows-7-vista-xp/
Note that obviously I don't have nVidia on my Lenovo ThinkPad X201s, I have an integrated Intel HD Graphics chipset that I think is on the same die as the i7 CPU. So my steps will be different, if they are possible at all.
The above link works OK and has genuine advice and I am not connected to the site in anyway. The link came from here:
http://www.tomshardware.co.uk/forum/14189-63-solved-display-driver-stopped-responding-successfully