I'm going to comment on an essay by the late Richard Gale. He was one of the more competent philosophical atheist. In this essay his primary target is freewill theism: R. Gale, "Evil as Evidence Against God", J. P. Moreland, C. Meister, & K. Sweis eds. Debating Christian Theism (Oxford 2013), chap. 15.
What, in general, is an evil and what are the different types of evil? An evil is something that, taken by itself in isolation, is an ought-not-to-be, an "Oh, no!" Examples are physical and mental suffering by a sentient being, including lower animals, immoral action, bad character, and a privation in which something fails to measure up to what it ought to be, such as a human being born blind. The qualification "taken by itself" is important, since some evils are justified because they are so-called a blessing in disguise, being necessary for the realization of an outweighing good or prevention of an even greater evil. As members of such a larger whole, they are not an ought-not-to-be.
In some respects that's a good definition. However:
i) To say congenital blindness is a natural evil is a teleological judgment. But naturalistic evolution rejects final causes. If there's no telos, there's no dysteleology. Congenital blindness is only a natural evil if the eyes were designed to see. But naturalistic evolution is a nondirective process rather than a goal-oriented process. Eyes have no purpose in naturalistic evolution.
ii) How much mental and physical suffering do lower animals experience? And is that a natural evil? Notice how some animals deliberately seek out what looks like a painful experience. Like lions fighting for control of the tribe. If it's excruciating, why don't they avoid it?