I used to deal with a similar issue. Remember to take a Vit. D supplement in the winter. Many nutritionists don't agree that the recommended 400 IUs is nearly enough. I have to say that I agree through my own experience. 15 min of direct sunlight is enough to produce 1000 IUs so you can certainly take more.
Scrutinize your diet to make sure you are getting enough iron.
But the BIG THING with me and my (gone) fatigue was loss of muscle mass- which I thought may have been depression or low thyroid after losing 60 pounds.
So the question is... are you in a calorie deficit?
Being in a calorie deficit (i.e. losing weight) means that your body will take those missing calories for normal maintenance from A. Glycogen stored in liver, B. Body fat and C. MUSCLE.
After glycogen stores, do you know which one your body will preferentially catabolize?
It's NOT body fat. It's muscle mass. And I don't mean the result of natural atrophy do to losing weight. It's actively and preferentially being catabolized for energy when you are in a calorie deficit.
Resistance training made me feel so much less lethargic after only 2 weeks because it rebuilt the muscle and kept my body from using it as energy. Now I can WALK! And it doesn't feel like moving a mountain to take a damn step! Try it. And don't use those silly 3 pound weights either. Start with some basic weight lifting moves and lift the heaviest you can manage. That means, don't touch that 5 pound dumbbell!
But otherwise, yes, physical exercise definitely makes me want a nap.