I was asked why low carbs have a tendency to make folks have low energy.
Simple answer...they aren't eating enough fat. Most likely, they are severely undereating fat.
Here's an article that can explain it better:
Why Low-Carb Diets Must Be High-Fat
The case for getting energy from fat and ketones
When most people think of eating a low-carb diet, they tend to think of it as being a protein-based one. This is false. All traditional carnivorous diets, whether eaten by animals or humans, are more fat than protein with a ratio of about eighty percent of calories from fat and twenty percent of calories from protein. Similarly, the main fuel produced by a modern low-carb diet should also be fatty acids derived from dietary fat and body fat. We find in practice that free fatty acids are higher in the bloodstream on a low-carb diet compared with a conventional diet.[vii] [viii]
But fats also produce an important secondary fuel: 'ketone bodies'. Ketones were first discovered in the urine of diabetic patients in the mid-19th century; for almost fifty years thereafter, they were thought to be abnormal and undesirable by-products of incomplete fat oxidation. In the early 20th century, however, they were recognised as normal circulating metabolites produced by liver and readily utilised by body tissues. Ketones are an important substitute for glucose. During prolonged periods of starvation, fatty acids are made from the breakdown of stored triglycerides in body fat.[ix] On a low-carb diet, the fatty acids are derived from dietary fat, or body fat if the diet does not supply enough. Free fatty acids are converted to ketones by the liver. They then provide energy to all cells with mitochondria. Within a cell, ketones are used to generate ATP. And where glucose needs the intervention of bacteria, ketones can be used directly. Reduction of carbohydrate intake stimulates the synthesis of ketones from body fat.[x] This is one reason why reducing carbs is important. Another is that reducing carbohydrate and protein intake also leads to a lower insulin level in the blood. This, in turn, reduces the risks associated with insulin resistance and the Metabolic Syndrome.
Ketone formation and a shift to using more fatty acids also reduces the body's overall need for glucose. Even during high-energy demand from exercise, a low-carb diet has what are called 'glucoprotective' effects. What this all means is that ketosis arising from a low-carb diet is capable of accommodating a wide range of metabolic demands to sustain body functions and health while not using, and thus sparing, protein from lean muscle tissue. Ketones are also the preferred energy source for highly active tissues such as heart and muscle.[xi]
All this means that more glucose is available to the brain and other essential glucose-dependent tissues.