Mike, with due respect, I think you’re misunderstanding the way LCHF works. You must be in caloric deficit to lose fat. There’s no way around that. Maybe there’s some crazy biochemical exception to that rule, but in general, CICO is technically accurate. It just doesn’t explain why people get hungry when, for instance, they’re in calorie surplus.
There’s been some debate over the mechanism by which LCHF seems to work such magic, at least in very overweight people, but a simple explanation is that fat satiates, and by removing the carbs you’re reducing insulin levels and therefore reducing hunger signals. Which means that an obese person who begins eating LCHF will suddenly find that they’re a lot less hungry and will rapidly be satiated while in caloric deficit – thereby enabling fat loss.
Nowhere in the Carbohydrate-Insulin Model is there a suggestion, as far as I know, that fat-burners don’t need to be in caloric deficit to lose fat.