In The Problem of Pain, Lewis grapples with the problem of suffering in a world creating by an ultimately good and powerful God. Before doing so, however, he sets the stage, providing background information on what he perceives to be the origins of religion. In the first section, he gives three elements of religion, and a fourth that characterizes Christianity: the Numinous (akin to awe-inspired dread), some sort of morality system, and a combination of these two; the Christian fourth element is Jesus.
The second chapter is where Lewis starts to address the actual question at hand: if God is both omnipotent and all-good, why is there suffering in the world? He begins by investigating the nature of omnipotence: it does not mean the power to enact nonsense, or do things that are inherently self-contradictory. The things that happen in creation are in essence the only things that could have happened, making this the only possible world, as God is infallible, so there must be some explanation for his reasoning, although it's likely that we won't know that until we die.
But how could a good God knowingly create a universe that is full of evil? Lewis brings up the insightful objection that our morality is not the same as God's morality: being finite and flawed, the human mind cannot grasp the knowledge of God, so it is a ridiculous assertion that God did something wrong or unwise. Furthermore, Love is not the same as making someone happy, and the universe does not revolve around Man. God alone has complete knowledge, and his love for mankind does not allow him to merely abolish suffering, as even pain has beautiful usage.
Another reason people don't understand the need for suffering is that they don't understand their own problems. They believe that they're decent people, and they've done their duty to society and whatnot, but they don't realize the steady undercurrent of sin that dominates their hearts. This brokenness is not God's choice, but the result of the free choice of man, who, being made in the image of God, has free will to choose between good and evil, choosing the latter. Our present condition, therefore, is not God's fault, but our own.
In Chapter 6, Lewis really gets into the heart of the titular issue by addressing human pain. He considers the question of whether suffering is necessary to produce good. In this broken world, he argues, suffering is indeed necessary for turning toward God. Doing so involves giving up the self and adopting the nature of God, which is a painful process for sinful humanity. This pain is uncomfortable at the time, but like children, we will eventually be grateful that we went through it, as it taught us invaluable lessons. Experiencing suffering makes it easier to go through more suffering to give up the self, as Christ intends for us to do. Suffering isn't good as itself, but as a means to an end; in context of the purification process, suffering is a necessary step, but one with immense power of cleansing.
At first glance, the existence of Hell seems to imply that God is limited in either power or goodness. Lewis argues, however, that although the idea seems intolerable, it's actually necessary; humans have free will to choose between themselves and God, and if they choose themselves, they need to be able to stick with that choice - thus the necessity of Hell. Hell isn't retributive punishment, but God allowing humans the life they truly desire.
After tackling the bulk of the argument in his sections on human pain, Lewis then addresses the issue of animal pain. Since there doesn't seem to be a purifying value in that, since animals don't have souls, doesn't this prove that suffering is meaningless and therefore God can't be all-good? Actually, animals don't have any concept of sequential consciousness, so they aren't really aware that they're suffering. The exception, of course, is animals with higher levels of intelligence. Lewis's tentative answer to that confusing question is that these animals might be present in Heaven; otherwise their suffering seems useless. But we're finite humans; what do we know?
Heaven, the antithesis to Hell, exists as a place where humans can gratify their deepest desire: to behold God for eternity.
