A ketogenic diet will help better than burning carbohydrate will. If you want to put on muscle, remember that you need a fairly high protein intake, one that includes the branched-chain amino acids. The essential BCAA’s are leucine, iso-leucine, and valine, so eat plenty of foods that contain them (Google will tell you).
People reading this post should bear in mind, however, that for folks who are not building muscle, BCAA’s in quantity can cause systemic inflammation, which is not generally a good idea. (A small amount, especially of the essential BCAA’s is fine, however.)
Now, as to how much protein, the keto experts’ recommendations generally vary, but they tend to fall in the range of 1.0-2.0 g/kg LBM/day. Putting on muscle means eating at the top end of that range. So if your lean body mass is, say, 90% of your weight, then you probably want somewhere in the vicinity of 64 * 0.9 * 2.0 = 115.2 g of protein a day, or around 460 g of meat. (Most meats are approximately 25% protein.) There is a fair amount of leeway here, so it doesn’t have to be precise. Listen to your body.
But the key is keeping that carb intake to less than 20 g/day and filling in your calories with fat. The best guide to how much to eat is your appetite, especially once you’ve been eating a ketogenic diet for a while, do eat when you get hungry, stop eating when you stop being hungry, and don’t eat again until you are hungry again.