I hesitated to replay so I can await of what you eat. Fair enough, you've adapted the lifestyle of low-carb pretty well; maybe too well. By your diet, I can see how you may feel light-headed during strength training and not during other types of training, and that has to do with the usage of your energy systems. Anerobic burns energy without any oxygen (primarily sugar) and aerobic burns energy using oxygen (primarily fat). Resistance training uses the former, which can be the reason why you might feel dizzy doing so due to lack of glycogen storage, while the latter is fine to you because it's able to give you a constant supply of fuel from your fat stores.
However it is still possible to weight train while still maintaining fairly the same diet; just by decreasing the volume, and in return, increase the intensity (ie heavier weights, less reps), by doing so, it decreases the lactic acid buildup that causes the majority of the problems, while still achieving some progress.
Originally Posted by Fish-and-Chips-Yum
It really just rubs me the wrong way when people try to cheat out how the body is supposed to work. Your body was intended to run on carbohydrates, as well as proteins and other nutrients in a balance. Any sort of extreme diet will have repercussions in the long run, whether it be in 5 years, 7 years, or 35 years. If you're still adamant about doing this diet then I wish you the best of luck, though I want people to be aware that just because something works now, it doesn't mean it's perfectly safe with no cost.
The body does run on glucose, but how it gets it can be obtained from either carbs or body fat (via beta-oxidation). It also runs on keytones, which is powered through fat and protein when in ketosis (prolonged fasted state, or lack of glucose). I think the general public is stuck to the direct relationship between carbs and glucose, neglecting the body's ability to burn fat into energy, and how insulin can prevent two things from doing so. At first I was stuck to that thought of the direct relationship between carbs and glucose, then took me a couple of years of anecdotal and behavioural studies of diets outside realized that the body is more better off eating off the lifestyle where agriculture and industrialization didn't exist, and that consisted of whole foods and unadulterated meats (in an ideal secnario, I would try to eat all my meats organic, but it's so damn expensive).