No fat, assuming a calorie restricted diet of course. If you eating enough calories, then you won't burn lean muscle mass on a low fat diet, but then you won't burn fat either.
Once you start to restrict calories your body has to look elsewhere to get its energy. The main arguement is don't give it any fat, or very low amounts so it starts to look for it in the
adipose tissue.
If you give it lots of carbs, say 70% then obviously it doesn't need to burn muscle for carbs as you are giving it lots right? Well no because you are still in a
calorie deficit, and your body needs to get energy from somewhere and it is set up to do so from carbs as that is all you are giving it.
This is why the most efficient diets for burning fat are essentially 100% fat diets. On such diets your body switches over to burning fats as the primary source of energy and thus it readily burns body fat for energy happily as that is what it is set up to do.
This of course is not a good diet in general as you are not giving yourself enough protein to maintain lean body mass, so your muscle tissues will start to degrade. Not becuase they are being broken down for energy, but because there is nothing to upkeep them.
So a more realistic diet is 70% fats, 30% proteins. This will strip off fat massively fast, especially if the fats are highly ketogenic / thermogenic (omega-3, medium and short chain TG's).
Such a diet is however very difficult for most people to follow as the meals are very unfamiliar, and you can't eat what you are used to normally. A lot of people also eat really unhealthy fats (rancid when bought because of improper storage) and burn them when cooking so they are highly oxidized.
It is also easy to get constipated due to lack of fibre, and vitmain and mineral supplementation may be necessary depending on the quality of the meat. If you eat quality organic organ meats it won't be.
Thus a more optimal diet still would be 65% fats, 30% protein, 5% carbs. With the carbs being very nutrient dense, very fiberous ones. This is essentially any ketogenic diet which is about ~100 years old.
The fat burning advantage is also given an extra boost in that there is an inherent ketogenic low efficiency for most people so that you burn more fat calorie wise that you would if you were using carbs, meaning you lose more weight on isocalorie diets. That is essentially the main Atkins arguements, and you can find studies which support this metabolic advantage.
It is a pretty radical diet though and prone to problems mainly because of incorrect applications, but can work very well especially for people with syndrome-x or similar problems with carbohydrates.
In general though I would probably first suggest that someone wanting to lose weight try :
1) exercising more, both cardio and resistance
2) removing all quick junk foods and refined foods
3) increasing fibre intake
4) splitting up meals
5) drinking more water
And eat a balanced diet, decent servings of hihgly ketogenic/thermogenic fats, slow digesting proteins and low GI carbs. If this fails to work then there are many reasons why it can (thyroid for example), then a high fat ketogenic diet might work so look into that.
-Cliff