Several studies suggest that eating a low carb diet can keep weight low because it, in effect, restricts calories. The argument goes that people feel fuller at a given volume of calories when the calories are comprised of protein and fat than when comprised of carbohydrates.
This may be true (but I doubt it)...
...which means that the program would meet one of the two elements of healthy CR, i.e. the restriction of calories. But that is only half the plan. CR requires, in addition, that the calories consumed be especially nutritious. As a practical matter, that means that the diet must include copious fruits and vegetables.
This is not something you see on “low-carb” diets. The centerpiece of every low-carb diet that I have seen is animal based, i.e. fats (saturated) and protein. These are not nutrient-dense foods. Furthermore, a plethora of studies exist suggesting, if not clearly establishing, a link between animal-source foods and cancers, heart-disease and diabetes. A good summary of this is found in “The China Study” by Colin Campbell. Also Google the terms under research.
The safest approach to CR is to stick with calories comprised of plant foods (especially raw) with animal products being no more than an occasional component. You will find that you are eating such a large quantity of food that you should rarely feel hungry. By contrast, animal foods are comparatively calorie-dense and nutrient-sparse.
The weight loss on such programs probably has less to do with calorie restriction than the questionably healthy and little-understood effects of ketosis--a complex process by which the body is forced to consume its fat stores for energy. This is a metabolic survival response normally associated with starvation which, when recommended as a weight loss strategy, should at least raise some intuitive red flags for even the least informed aspirant to health and longevity.