Are there more than just the one? Could be a fungus, virus or just the simple fact that not all buds will complete the bloom cycle. Your photo shows an Asiatic Lily that looks healthy other wise.
I am wondering if it is a nutritional deficiency and is aborting the buds. Your foliage looks a little on the light side. Do you add bonemeal or bulb food to it? is it growing in a container? if so it really needs to be fed more than if it was in the ground.
I get that on my lilies too, every year, and they're well fed. It could be a bug that has snacked on the buds. Another possibility is too dry or too wet weather. Those lilies want it perfect, primadonnas that they are.
