No, they won't go away themselves with time.
If you want to have them removed, you must have a surgery.
If you want to have your cholesterol deposits cured, you have to change your lifestyle and have surgeries.
The dermatologist remove them by laser burning the upper layer of your skin(needs local anesthesia). You may need not only one time but repeated laser procedure before the deposits are totally removed.
Change your diet by having better food and try to loose weight.
Usually the cholesterol deposits will not go away with the time which is caused by the large amount of the fat store. You'd better use the oil essentials to adopt on the surface of the eyes to release the symptom of the eyes. You should eat more food with vitamin C and A to make the eyes get moisture and become comfortable. You should have the good rest to avoid the dark circles under the eyes.
Well, generally speaking, it is normal to have them, and they are painless lumps under the skin of your eyelids, usually on the upper surface closer to your nose. In common, they will grow over a period of a few months. To remove it, you can just have cosmetic surgery acid, liquid nitrogen or carbon dioxide. And they can be detected easily. Of course, you should know that even after removal, they might grow back. In my opinion, you could see your doctor for a biopsy if a growth on your eyelid does not disappear after a few weeks. Anyway, just have a try.