"Simply put, there is no option for weight maintenance that is simultaneously low in carbohydrate and low fat. Your energy has to come from somewhere, and for people with carbohydrate intolerance, their best (and safest) long-term energy source is dietary fat. ... Our point here is that with your dietary carb intake constrained by your individual level of carbohydrate tolerance (be it 40 or 100 grams), you must get comfortable eating fat as your primary source of dietary energy if you want to succeed in low carb maintenance."
Jeff S. Volek and Stephen D. Phinney