Alright, so you can lose weight fast with a low-carb diet. The lack of carbs will send the liver and muscles for their glycogen storage using up water and stimulating increased production of urine, or polyuria (1). Along with the osmotic diuresis, or increased urination, will be loss of sodium and potassium (1-2).
Couple that with a change of diet that eliminates water-retaining carbohydrates and foods high in potassium and water (such as fruits), and the diet could lead to dehydration and othostatic hypotension as well as potassium deficiency (1-2). Fatigue sets in due to used up glycogen stores (1). Exacerbating these potentials are appetite suppression and possible vomiting resulting from nausea, common in low-carb diets, which can lead to more depletion of electrolytes (1).
Even a moderate deficiency of potassium can increase calcium excretion, elevate blood pressure and cause abnormal bone turnover (2p455). If hypokalemia occurs from heavy loss of potassium (such as from vomiting), then there would be an increased risk of cardiac arrhythmia, muscle weakness, irritability, hypercalciuria, glucose intolerance and mental disorientation (2p455).
Potassium supplements can correct potassium deficiency, but too much can be toxic, producing hyperkalemia, which can lead to severe cardiac arrhythmias and cardiac arrest (2p455).
References
1. Hirschel B. [Dr. Atkins' dietetic revolution: a critique]. Schweiz Med Wochenschr 1977;107:1017-25.
2. Gropper SS, Smith JL, Groff JL. Advanced Nutrition and Human Metabolism. Belmont, CA: Thomson Wadsworth, 2009.