Indeed, Jonathan! That is another possible response to explain the Problem of Evil. One which I wish I'd had the time/space to explore as well. 

Augustine of Hippo maintained that since God is perfectly good and all-powerful, there is no way he could create or allow evil in the world. So he is attributed with the development of the idea that evil is simply a lack of good. (I believe it could also be phrased like you said-- as a lack of God. Since God is the greatest manifestation of goodness and love.)

"In the bodies of animals, disease and wounds mean nothing but the absence of health; for when a cure is effected, that does not mean that the evils which were present—namely, the diseases and wounds—go away from the body and dwell elsewhere: they altogether cease to exist; for the wound or disease is not a substance, but a defect in the fleshly substance—the flesh itself being a substance, and therefore something good, of which those evils—that is, privations of the good which we call health—are accidents. Just in the same way, what are called vices in the soul are nothing but privations of natural good. And when they are cured, they are not transferred elsewhere: when they cease to exist in the healthy soul, they cannot exist anywhere else." -- Augustine of Hippo

Thank you for reading and adding your thoughts!