Yes you can eat only fat and meat in excess and lose weight.
I have seen steady weight loss with a massive abundance of calories (5000 calories a day, 80%+ fat) with zero exercise. The experiment was undertaken to check this exact theory.
Fat storage is all about the carbs, not fat.
The "Seven Deadly Sins"
• Grains (wheat/rice/oats etc) . . . . . • Dairy (milk/yogurt/butter/cheese etc) . . . . .• Nightshades (peppers/tomato/eggplant etc)
• Tubers (potato/arrowroot etc) . . . • Modernly palatable (cashews/olives etc) . . . • Refined foods (salt/sugars etc )
• Legumes (soy/beans/peas etc)