Lewis here addresses the age-old seemingly insoluble dilemma regarding man's free will and the sovereignty of God.
Is God truly sovereign--that is, is He fully directing all events to achieve His ends and His will? If the answer is yes, then that leads to the conclusion that no one truly has a free will. Whatever you "decide" to do was in actuality determined ahead of time by God. How, then, can God hold people responsible for their sins if He knew and/or determined ahead of time what sins they would commit--thus leaving individuals with no choice in the matter?
On the other hand, if you answer no, then how can God ultimately be in charge? His will would consistently be being violated by people making decisions--even minor, "unsinful" ones--that would frustrate that will. If it's God's will for me to do a certain thing but I exercise my free will and do something else, what then? Haven't I frustrated His plans?
Most Christians come to the conclusion that both God's sovereignty and man's free will exist side-by-side. The fact that they seem to us to be mutually contradictory is only because we are incapable of having God's level of comprehension of reality. (In Book 4, Chapter 3, "Time and Beyond Time," Lewis returns to the idea that God doesn't see things--even something as elementary and seemingly self-evident as the passage of time--as we do.)
Here are two examples from well-known Bible teachers from the past who have commented on this issue.
Nineteenth-century pastor Charles Haddon Spurgeon: "God . . . saves man by grace, and if men perish they perish justly by their own fault. 'How,' says some one, 'do you reconcile these two doctrines?' My dear brethren, I never reconcile two friends, never. These two doctrines are friends with one another; for they are both in God's Word, and I shall not attempt to reconcile them. If you show me that they are enemies, then I will reconcile them. . . . There are many things in God's Word that are difficult, and that I cannot see, but they are there, and I believe them. I cannot see how God can be omnipotent and man be free; but it is so, and I believe it. 'Well,' says one, 'I cannot understand it.' My answer is, I am bound to make it as plain as I can, but if you have not any understanding, I cannot give you any; there I must leave it. But then, again, it is not a matter of understanding; it is a matter of faith. . . . If they appear to contradict one another, they do not really do so, because God never contradicts himself" (Sermon #241, delivered on Sunday, January 16th, 1859, at New Park Street Chapel, Southwark).
Bible expositor Charles Simeon: “The author is disposed to think that the Scripture system is of a broader more comprehensive character than some very dogmatical theologians are inclined to allow; and that, as wheels in a complicated machine may move in opposite directions and yet subserve one common end, so may truths apparently opposite be perfectly reconcilable with each other and equally subserve the purposes of God in the accomplishment of man’s salvation” (quoted in H. C. G. Moule, Charles Simeon, 79).
No matter where one comes down on the issue, the Bible clearly teaches both concepts. Look here for an extensive list of verses dealing with God's sovereignty (i.e., predestination and election). And verses below (emphasis added) are among those that point to man's having free will.
John 7:16-17 (ESV): So Jesus answered them, "My teaching is not mine, but his who sent me. If anyone’s will is to do God’s will, he will know whether the teaching is from God or whether I am speaking on my own authority.”
Romans 1:19-21 (ESV): For what can be known about God is plain to them, because God has shown it to them. For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. For although they knew God, they did not honor him as God or give thanks to him, but they became futile in their thinking, and their foolish hearts were darkened.
James 4:1-2: What causes quarrels and what causes fights among you? Is it not this, that your passions are at war within you? You desire and do not have, so you murder. You covet and cannot obtain, so you fight and quarrel. You do not have, because you do not ask.
Both Concepts Combined
2 Samuel 10:12: Be of good courage, and let us be courageous for our people, and for the cities of our God, and may the LORD do what seems good to him."
Romans 9:17-20: For the Scripture says to Pharaoh, "For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth." So then he [God] has mercy on whomever he wills, and he hardens whomever he wills. You will say to me then, "Why does he still find fault? For who can resist his will?" But who are you, O man, to answer back to God? Will what is molded say to its molder, "Why have you made me like this?"