Carbohydrates are the brains source of energy, they're also one of our main energy sources overall. People on very low carb intake diets sometimes can be more tired than some.
You may not be getting enough iron if you're protein intake is down as well. Are you eating enough dairy? Low-fat dairy, especially yoghurt (i have found anyway) is a good source of protein for me.
Sleep is another factor, make sure you are getting your 8 hours a night
At what times are you feeling most tired? It's normal to have a "slump" period in the afternoon, mines usually around 4-5pm.
Is your calorie intake sufficient to cover your body's basic needs? You need to consume a minimal amount to maintain your body's function! I think it's strongly recommended you dont go under 1000 calories a day, and most people can go to 1200 and still lose at a decent rate.
Are you pushing yourself too hard? Exercise is well and good, but over-doing it can be just as detrimental to your health as doing none at all!
Ummm...thats about all I can think of offhand. I follow a relatively high-carb/low fat "diet" myself. I'm not on any plans, just altered my own eating habits to healthier options. I tend to eat a LOT of fruits & veges, as well as wholegrains and a lot of low-fat dairy (yoghurt, skim milk etc). So i guess it's in a sense almost the total opposite to you lol. But i hope some of these suggestions help, and if all else fails, go see your doctor!