I think the medical community would have been able to spot and prove that theory if that was the case.
You say it's not about my theory and cure of getting more calories, but my cure theory is not just getting more calories, but specifically more CARB calories.
You chose the path of low-carb diet. Even though that diet is high in calories per volume, many experience tiredness and sluggishness and have to resort to stimulants, such as coffee, because that diet, as its name states, is low in carbs, the body's main and preferred source of energy.
If you're still feeling tired and sluggish, I recommend you try out a high-carb/low-fat diet in sufficient calories to see if that makes a difference before you continue with your theory.
I hope you stick around because I like your mentality of trying to find the root of the problem.