It is possible but only if you get fully into Ketosis, check with the urine test sticks that you're in, they turn dark purple.

Otherwise you're in a no carbs, no fat burning, no energy, no mans land of hell.

I wouldn't expect to be hitting any PBs though mate.

A lot of elite bbers sweat by keto diets. Personally I think they do work. Idk much about Atkins but if i were to recommend a keto regimen to someone it would be Body Opus or the Metabolic Diet. Both are great. So to answer your question. It is highly difficult but possible to build muscle while on low carbs but it really would come.down to caloric intake. I'd suggest you do a search on both diets I listed.

You cannot build muscle without carbs. Although it sounds good on paper, it doesn't work. First off, your body doesnt use carbs for energy, it uses glucose. Carbs break down to glucose very easy. do you know what else breaks down into glucose easily? Amino Acids (including Branch Chained Amino acids). Muscle is made up of 75% water and 25% amino acids. yes, some fat would be broke down into glucose, but why risk it? You cant cut out glucose, or you will die. Seriously! So many people think that low carb diets will make you make you lose weight. But just like any other diet, it comes down to how many calories you eat. Low carb it for a week or so and see how flat your muscles look. Then you say "i will carb up and get fullness", well why cut them out the other days? everybody will say how they lost weight so fast on low carb. And more than likely they did. Probably about 3 times as fast as a higher carb diet. Thats because 1g carb holds 3g of water. So you are losing weight, mainly water weight and some muscle and some fat(if your calories are low enough.). So are you trying to lose weight or lose fat? Low carb diets will also raise Myostatin levels, and inhibit mTOR pathways. Thats not good for guys wanting to get big. Not to mention how dead you will feel. And lets not forget the ketones. Ill let you look up the side effects of ketones. So do yourself a favor and eat some carbs.

lifting will keep you from losing what muscle you do have. you will also get stronger and feel better, i definitely recommend lifting.

If you are Type O or B blood, then yes, if you are A or AB then id find another diet.

Review this link:
http://nutrition.stanford.edu/projects/az.html

you wont build muscle as you are calorie defecient most likely. but you should always lift while trying to slim down. it help burn fat as you won't loose as much muscle as just dieting alone.

worst idea everrrrrr. why dont you try Keto?