When I was on a basic Low-Carb diet, I was very frustrated by the frequent high blood-sugar levels, particularly in the mornings. I eventually realised that my Protein intake was too high, and addressed this.
When I amended my diet to a truly Ketogenic/LCHF style (Low-Carb and no more than adequate Protein) these high levels, and Dawn Phenomenon, just disappeared. I am a sample size of one so maybe my experience/interpretation doesn't apply across-the-board, but I think that the basic biology backs up my experience.
The standard early-morning "liver dump", or Dawn Phenomenon, is via Gluconeogenesis - the breakdown of Glycogen in the liver into Glucose.
If you limit the amount of Glycogen by limiting the intake of Carbs and Protein, then the body has limited resources for Gluconeogenesis.
My interpretation of my own experience is that the body is careful to maintain a basic level of Glycogen in the liver, because Glucose may always be needed anytime for an emergency fight-or-flight situation.
In the case of a limited amount of Glycogen, the body will not waste this resource on the simple act of getting up in the morning.
In the case of plenty of Glycogen (and the body being trained that there will always be plenty more on the way soon) then the body will use this resource more liberally.
In my current Ketogenic/LCHF diet plan I keep to a daily limit of no more than 1g Protein for each 1 Kilo of my ideal body weight. This was mentioned in more than one of the books that I read on the Keto diet. When sticking to this, for me the Dawn Phenomenon never happens. For what it's worth, I interpret this as described above.
Excess Carbs and Protein that the body does not need immediately for energy or repair go to the liver to be stored as Glycogen (until the liver is full).
Regards,
Antony