When you start a low carb diet, you immediately lose a considerable amount of water weight. It's why people consider Atkins to be a scam (as they would immediately lose 5-10 pounds only to gain it back just as fast when they stopped dieting).

However, I have some personal experience eating low carb, and the rate of weight loss, for me at least, was around 2 lbs/week, as predicted by my food/calorie tracking app (MyFitnessPal).