I've been working really hard at getting my numbers down to the extent that I'm getting 4am hypos - 3mmol - fortunately a headache wakes me up but then stays with me for several hours! Is this something normal? Unfortunately I'm about a 1000 miles from my diabetic nurse atm!
		
		
	 
I get the very low BG in the early mornings.  I'm T2 on no medication, and as of April this year I won't have had a BG out of normal range for five years. The sweats etc. started around 2014/5, not sure. When it happens, I get nightmares and really extreme sweating - it happened last night after about a six week break.  Until I tried a CGM  a few years ago I had no idea that these sweats coincided with low BG, but they do. 
There isn't a great deal of knowledge about this, but I do know from my local low carb group that some non-diabetic people who've used a CGM have reported exactly the same thing: a sudden cliff-edge drop in BG that lasts minutes, if that, followed by a very steady rise that seems to turn into dawn phenomenon. There is some "confirmation" of this in research:
	
	
		
			
			
				
				Use of continuous glucose monitoring (CGM) is increasing for insulin-requiring patients with diabetes. Although data on glycemic profiles of healthy, nondiabetic individuals exist for older sensors, assessment of glycemic metrics with new-generation ...
				
					
						
							
						
					
					pmc.ncbi.nlm.nih.gov
				
 
			 
		 
	 
This piece of research is on non-diabetic people using a CGM, intended to establish a sort of baseline and an idea of what "normal" looks like in modern CGM use. You'll see towards the end in the "Discussion" section they mention that there were a number of these "very low BG in the early hours" incidents, which they found a bit baffling, the subjects being non-diabetic etc... 
It's often put down to "lying on the sensor" but I don't think that lying on the sensor explains what causes the sweats and nightmares - which are exactly what you'd expect from an actual low BG.  I think this is an attempt to "explain away" rather than to really explain what's going on. 
@Jasmin2000  suggested to me in another thread this fall in BG could equally be caused by a increase in insulin - but no-one seems to be interested in doing any work on it.