I tried not closing the lid, just pressing start button to suspend during intervals or overnight - no use, 3 more crashes.
I did find a note in my records re. the first event, which I associated with starting up without the external monitor (which was connected) being powered up - this was while I still had LL 3.4. So probably moving to 3.6 was not the problem, but of course I don't know.
In between crashes, LL is great, so I hope I can take time off over Christmas to research this problem. I will post here if I find a solution.
As always, re-starting gets it back working, though I've to enter long master passwords etc. again!