I have a low-protein, low-fat breakfast with wholewheat bread and fruit, and then I eat low-carb for the rest of the day. It works wonderfully! I am also allowed to have carbs for lunch every now and then, and for me that means if I want to have a piece of cake on the weekend - that's my lunch! 
I eat mostly unprocessed food (meaning I make most of my food myself from scratch), a lot of fish, some meat (mostly to keep my husband happy), lots of vegetables. The only thing I'm gonna miss are potatoes, because I love them and they are the only carbs I can't have for breakfast (but I might add them to my lunch when I'm in maintanance). Now I haven't got any weight loss to show, but I've only just started properly. But I do know I'll easily eat like this forever. It actually makes me feel great, I sleep better, my body already feels firmer (I seem to retain less water), and it makes me feel like I'm doing something really good for my health.
Low-fat or high-fat is subject to perception, I think. As I've always rather eaten food that is more "natural", I never bought low-fat cheese or stuff like that in the first place (with the exception of mozzarella, where I actually prefer the low-fat version). I eat regular cheese, I fry my food in a variety of vegetable oils and I still cut off the fatty bits of my ham. That is just a normal, healthy amount of fat to me. To someone used to a low-fat diet, it is probably high-fat.
But when you cut out lots of carbs, your body needs energy from somewhere else.

