Yes you can lose fat on a low carb because it’s just another low calorie diet. How do I know this? I’ve done low carb, (Atkins, etc) high carb, (Slimming Word) moderate carb etc and log my food and was shocked each time to see they were all low calorie. After the initial week or so the rate of fat loss is same as any other diet. It’s calories in calories out. Simple. It’s what some call indirect deficit diet placing silly restriction, rules can eat must eat etc. and of course you lose weight but nothing to do with low carb. It works because it’s a low calorie diet.
The original therapeutic diet for paediatric epilepsy provides just enough protein for body growth and repair, and sufficient calories[Note 1] to maintain the correct weight for age and height. The classic therapeutic ketogenic diet was developed for treatment of paediatric epilepsy in the 1920s and was widely used into the next decade, but its popularity waned with the introduction of effective anticonvulsant medications. This classic ketogenic diet contains a 4:1 ratio by weight of fat to combined protein and carbohydrate. This is achieved by excluding high-carbohydrate foods such as starchy fruits and vegetables, bread, pasta, grains, and sugar, while increasing the consumption of foods high in fat such as nuts, cream, and butter. Most dietary fat is made of molecules called long-chain triglycerides (LCTs). However, medium-chain triglycerides (MCTs)—made from fatty acids with shorter carbon chains than LCTs—are more ketogenic. A variant of the classic diet known as the MCT ketogenic diet uses a form of coconut oil, which is rich in MCTs, to provide around half the calories. As less overall fat is needed in this variant of the diet, a greater proportion of carbohydrate and protein can be consumed, allowing a greater variety of food choices.
On a ketogenic diet, your entire body switches its fuel supply to run mostly on fat, burning fat 24-7. When insulin levels become very low, fat burning can increase dramatically. It becomes easier to access your fat stores to burn them off. This is great if you’re trying to lose weight, but there are also other less obvious benefits, such as less hunger and a steady supply of energy. This may help keep you alert and focused.