To clarify, by a low carb diet, I do not mean ketosis, which is a very low carb diet (<20g per day). During ketosis, you don't need glucose as your primary source of fuel; it is rather the ketones that fuel you. Ketones, especially, BHB are muscle-preserving.
Now on to the actual question: Since low carb diets don't activate ketone production, the body most likely burns off the small glycogen storage that you have on when you do heavy resistance training or high intensity workouts. Thus the next alternative for providing fuel is gluconeogensis, the formation of glucose from proteins. Now assuming that you are eating adequate amounts of protein based on your activity level, will your body breakdown the protein that you consume first, or will your body break down your own muscle tissue first in order to initiate gluconeogenesis?