Please use your terms correctly. Lipolysis is to fatty acids as glycogenolysis is to glucose, and fatty-acid metabolism is to fatty acids as glycolysis is to glucose (notice, please, that the terminology is not parallel). We used to have another member who made this exact same mistake, and the error in terminology causes a great deal of confusion.
So the process of lipolysis, which is the breakdown of triglycerides into glycerol and three fatty acids, has been pretty well elucidated. It is mediated by hormone-sensitive lipase, which is inhibited by insulin above a certain level. Since triglycerides are too large to pass through the walls of adipocytes, they must be lipolysed in order to get in or out. Elevated insulin encourages fats to get into adipocytes, but once they are inside, its effect of inhibiting lipolysis traps them there. Lowering serum insulin is required in order to allow lipolysis, let the fatty acids out of the cell, and get them to cells that need energy, so that they can be broken down by the further process of fatty-acid metabolism.
Now the process of fatty-acid metabolism, which is the equivalent process to glycolysis, is also pretty well understood. If you can come up with a description of that process that does not involve the production of acetoacetate or β-hydroxybutyrate, that would be remarkable. I could believe that a genetic variant might interfere with the process of halting fatty-acid metabolism at the point where ketone bodies are produced, but not that the process doesn’t produce them.
If the paper you are reading doesn’t describe normal fatty-acid metabolism and elucidate specifically how that process avoids producing ketone bodies in Inuit with this genetic variation, then the authors are misinterpreting their data. I seriously doubt that gluconeogenesis is a robust enough process to feed the brain, even if the liver were to switch from using protein to using fatty acids as a substrate. And we know that the Inuit were not eating enough carbohydrate on their traditional diet for dietary glucose to be adequate to the purpose, either. Though I suppose it is possible (though not likely) that the blood-brain barrier in the Inuit is capable of passing molecules as large as triglycerides so that the brain could use full-on fatty-acid metabolism, but no one seems to be arguing that.