I had the same issue with sluggishness and found I just couldn't lift any weights while eating LC. I added potatoes (of all kinds) and 2-4 pieces of fruit per day back into my diet: NO body fat gain at all, and I have a lot more explosive energy during sports.
I totally back LC eating at first, but once the body "evens out" (hormone resistance, etc) you should be able eat plenty of whole food carbohydrate sources. Some HG tribes subsist on high carb diets without being over weight because they eat natural sources (ie they're not eating grain based, seed oil and added sugar "health food" that has been sprayed with vitamins).
The best way to find out? Try it for a month and record the results.