I'm not an expert by any means, but I am going to be starting a powerwalking / jogging regimine as soon as it's a little nicer. I am on a LC WOL and love it, I will never divert from this WOE, however, I had the same concerns as you. From what I gather, people who LC increase their carb consumption just prior to running (i.e. a bowl of berries in my case or a shake) and that should help with stamina, just see how your body reacts, we're all different - I don't think I'd need much more because I work out 3 x a week and keep my carbs at 20 grams per day and my calories around 1300 - 1500.

Hope this helps.

Vikki