If she's carrying excess weight, that in itself could make her lethargic. But also, if there is some underlying health problem, that could make her tire quickly. If she has joint stiffness, that could put her off exercising. Has she any other health problems?
However, if it's just a weight issue, then it becomes a catch-22 situation. The heavier she gets, the more she will tire easily when exercising, the less she exercises, the fatter she will become. And so on.
Different breeds of dogs have different exercise requirements, (a toy breed will not need as much as a Border Collie, for instance) but they all do need exercise. The kind of exercise which is sustained, for at least a 1/2 hour at a time, and not just once a day, (depending on need) a portion of which will raise the heart activity, is the usual daily exercise need of most dogs, unless they are very young, very old, or suffering from some infirmity or illness where exercise like that is not a good idea.
Corgis are great dogs, full of character. But unfortunately, owing to breeding, their over-short legs do take a lot of strain, and they can have problems sometimes. Likewise, Shepherds can get hip problems. And excess weight only makes this worse. So I would make sure there is no underlying joint trouble going on.
The next thing is to make it your mission to get some of that weight off her, now, before joint problems DO show up, as they almost certainly will, if the weight continues to be an issue.
I am certainly not a canine nutritionist, so can only give you a vague outline of what to do. You would be best to research this, or ask your vet. And, if there are any other health problems (like diabetes, etc) then be careful. But if she is a healthy mature dog (not too old) I would start by semi-fasting her for a couple of days! Dogs in the wild, and wolves, are accustomed to going without food for periods of time (a day or so) It has been suggested that in the Civilized Western world, we over-feed our dogs generally, and that can cause many problems. Dogs are Predators, not Grazers. Predators need to eat less frequently than grazers (ie cattle, sheep, and deer) Because we as humans, need three meals a day, or often eat every four hours or so, that does not mean it is a good idea for dogs. As a rough guideline a mature dog usually needs two meals a day, with about 7-8 hours in between. The more active a dog is, the more food can be given at mealtime. The less active, the less food.
Rule of thumb: Look at your dog's body. You can easily tell whether you are under, or over-feeding by the shape of your dog, and re-measure the mealtime portions accordingly. There should be a slight 'tuck' in the waist area. The ribs should be easily felt (though not seen). The shoulder/chest area should not look 'padded'. You should be able to just feel your dog's hip bones, but they should not be prominent.
For the semi-fast, maybe you could boil up some chicken (with bones), rabbit or fish (unseasoned) then when it is cooked, strain off the water. (Strip the cooked meat off the bones -By the way, NEVER give your dog fish, rabbit, or chicken bones! -and keep cool for later) When this water cools it will often form a light jelly. This is very nutritious. For the first day I would give her only this. And make sure there is plenty of fresh water too.
On the second day, add a little chopped meat/fish this time to the water.
On the third day, you could add a little rice too.
I can almost promise you that by the third day she will be more active, her appetite will be sharper, and she will look more 'alive'. She might not have lost very much weight, but if, after that you begin to feed her smaller portions twice a day, and no treats at all, she will soon get slimmer.
For the future, you could try a healthy-option dry dog food (I can't tell you which brand as I live in the UK and we have different products here) And add a little unseasoned cooked meat to the dry food at mealtimes to give her variety.