I don't want to tell u what to do, but I wouldn't diet like that AND work out. Like stated, without carbs your workouts will be pointless. Also, carbs are required to replenish your glucose levels. Your muslces use glucose as u work out, when ur muscles dont want to lift anymore its in part because ur glucose levels have been depleted. Imagine without carbs.
In my opinion, just eat healthy. I started working out about a year and a half ago. I don't take supplements or drugs because I despise them really, I want to be all natural. Over time, as your body builds muscle mass, with or without dieting, you will lose weight(unless u eat horribly). Cut the junk food out, consume things that are healthy and you will definatly love the results. Make sure to eat a large amount of protein AND carbs(sugar doesnt count, grains do!) if you are serious about lifting weights. Also don't forget vitamin C, you need alot, we all do. Drink alot of milk as it is loaded with protein and calcium(required for muscle function as well as bone density.)
Sorry if i described a diet that you don't want to do, but I don't think atkins would be good while working out. The way I see it, if it's natural, eat it. The majority of synthetic things are loaded with crap that strain your body.