I'm sure that not everyone is satisfied with either of the answers given by Lewis. The question remains, for many.
One of the books of the Bible, Job, is about suffering. God, although sovereign, allowed Satan, the adversary, to take Job's possessions, his children, and his good health. (Satan said that, if he was allowed to do so, Job would lose his faith in God.) Job didn't like all this loss, and complained about what he didn't like for a few chapters. Other people, well-meaning, tried to tell Job that all this was his fault -- he must have done something bad. His wife told him to stop believing in God. Job refused to believe that his troubles were his fault, and he refused to stop believing in the goodness of God. But he still had a question. Why did this happen to me? In the end, God appeared to Job, and, basically, said, "Who are you to question me?" Job said, basically, "I'm sorry, you are right. Forgive me. I'll shut up." Then God restored his possessions, and he had more children. God told those who had questioned Job's righteousness to ask Job to pray for them. Satan doesn't make an appearance, after the very first part, but presumably he was seriously disappointed by Job's reaction. In many ways, the answer given Job is the same as the answer given in The Problem of Pain.
I don't know, for sure, if Job was a real character. He probably was, but I suppose that the book could be a long parable. I don't think it matters, for our purposes. The question remains -- why is there suffering, if there is a powerful and loving God?
I presume that you know enough about the Harry Potter books, by J. K. Rowling, that what I am about to say makes sense. If not, you should read them, or at least the Wikipedia summary. (Here's one place where I have written about the books previously.)
Is J. K. Rowling a terrible person? After all, she wrote about a character, Harry Potter, who had to undergo a great deal of suffering. His parents died while he was still very small, he had to live with relatives, the Dursley's, who took advantage of him, and restricted him terribly. He went through all sorts of ordeals. Some of his best friends died. He felt that he and his two closest friends had to leave his wizard training at Hogwarts, and wander in the woods for an extended period of time, during which the three of them suffered the misery of disagreeing with one another, and doubting each other's motives. Harry's mentor, Dumbledore, died. Harry himself offered to die to save the good wizards.
Would people read these seven books, and watch the movies based on them, if Harry hadn't had to suffer? I don't think so. A life without conflict, without occasional misery, seems dull and uninteresting. (How much good news do you see on TV, or read in the newspaper, compared to scandals, natural disasters, wars, crimes, stupidity by various politicians, and other awful things? Not very much. The news organizations couldn't sell good news. We wouldn't buy it, or watch or read it.)
Rowling, to write a novel which speaks to us (or at least to some of us) included suffering, of various kinds. True, it wasn't all about suffering. In the end, Harry marries his sweetheart, and has children. He is at least on nodding terms with Draco Malfoy, who was once his bitter enemy. Voldemort and his followers are defeated. But I submit that Rowling, who had almost absolute power over the content of her books, including the plot, was not a bad person because she put many of her characters through terrible suffering. And she didn't put in characters, like Voldemort, who had, except possibly before the books start, no good characteristics, because she was not in control of what she wrote. She was.
Similarly, God is not a bad person, nor impotent, because there is misery in the world.
I know. The Harry Potter books are fiction. My life (I think) is real. So is yours. No analogy is perfect, and this one certainly isn't. But I think it helped me to write this post. Besides, I'm not so sure that the life of characters in a novel, in relationship to the author, doesn't resemble the relationship between our lives and the Creator.
Thanks for reading.