Unless your a newb it will be difficult adding LBM on a low carb diet. Weight training is a glycolytic activity, meaning it uses glycogen as fuel. You get glycogen from carbs and without them you burn yourself out pretty quickly.
The dizziness you experienced is most likely due to the 'transition period.' When you first start on a low carb diet there is an uncomfortable period where you lack mental ability, dizziness, headaches, lethargy and all that good stuff. After about a week of so, the symptoms should go as your body gets more adjusted to going into and staying in ketosis. Some people actually experience energy boosts and say they feel better, however an athlete, especially some who uses resistance exercises needs carbs to optimally train.
I tried a CKD then i tried a lower carb (50-100g/day) diet and didn't see any differences. I still incorporated re-feeds, which acted like a psychological break from dieting and boosted leptin etc. I also had more energy to train when increasing carbs.