I have started seriously weight training again, and I am finding the 20-25g carbs of Atkin's Induction/OWL is too low to allow me to lift effectively. I have started to eat a heavier carb snack about a hour before weight training, and it has helped. Mind you, I mean heavier carb in a LC sense- some strawberries or some nuts, real peanut butter etc. I have started making a protein shake to drink before working out with some strawberries or peanut butter, protein powder etc. I have a lot more energy, but I am not adding a lot of high GI carbs, so my blood sugar is not going nuts. Plus, those extra carbs are ones I am actively using, not letting sit in my bloodstream like I used to.

Also, as others have said, you might want to relook at your reps/sets etc. The more I research, the more I think that 10 reps is probably the sweet spot for beginners. you might want to do something simple like 2 sets, one warmup with 50% of your max weight, and then a second set at your full weight. I have been doing this sort of workout for a couple weeks and have seen good results, meaning I have had to increase my weights already.

One of the things that has concerned me a bit with Atkin's is that his books don't cover active exercisers very well. He has a couple pages here and there saying exercise is good, but no specific information for people doing serious training. I am not sure that "pure" Atkin's works well with people doing serious weight training as part of their exercise regimes.