An interesting study (J O Hill J C Peters G W Reed D G Schlundt T Sharp H L Greene. Nutrient balance in humans: effects of diet composition. The American Journal of Clinical Nutrition, Volume 54, Issue 1, 1 July 1991, Pages 10–17).
The purpose of this study was to examine the effect of alterations in diet composition on energy expenditure and nutrient balance in humans. Eight adults (three men, five women) ate a high-carbohydrate (60% of calories from carbohydrate) and a high-fat (60% of calories from fat) diet for 7 d each according to a randomized, crossover design. Six subjects were studied for an additional week on a mixed diet (45% of calories from fat).
For each subject, total caloric intake was identical on all diets and was intended to provide the subject’s maintenance energy requirements.
All subjects spent days 3 and 7 of each week in a whole-room indirect calorimeter.
Diet composition did not affect total daily energy expenditure but did affect daily nutrient oxidation by rapidly shifting substrate oxidation to more closely reflect the composition of the diet.
You can burn more fat and not lower your metabolism on a lower carb diet.