Be careful when combining low-fat with low-carb. It's safe to moderately restrict both, but it can be risky to drastically cut both fat and carbs.
Very low-carb and low-fat diets can result in what's called "rabbit-starvation," or sometimes "protein poisoning." It's called that because it was first observed in pioneers on wagon-trains, especially in the winter, where the only food source was rabbit and other very lean meats (protein, but very little fat or carbs)
Reportedly, people died faster (and sicker) than those who ate nothing at all.
The symptoms are pretty extreme, so as long as you know what to look for, and don't think being sick is a good sign, it's not something to be too concerned about.
But there recently was a woman who created a diet (which it turned out she didn't really follow herself - at least not for very long, because she used fake "after" pictures - and didn't lose the weight she claimked to). It was a varient of Atkins that reduced carbs and fat to nearly zero.
Many people got sick from her diet, and a few even died, because they believed her when she said that being sick was a good thing. In fact, she called it SNAT or SNATT and said it was a desireable state and proof that the diet was working (it stood for semi-nauseous, all the time).