Supposing there was no intelligence behind the universe, no creative mind. In that case, nobody designed my brain for the purpose of thinking. It is merely that when the atoms inside my skull happen, for physical or chemical reasons, to arrange themselves in a certain way, this gives me, as a by-product, the sensation I call thought. But, if so, how can I trust my own thinking to be true? It's like upsetting a milk jug and hoping that the way it splashes itself will give you a map of London. But if I can't trust my own thinking, of course I can't trust the arguments leading to Atheism, and therefore have no reason to be an Atheist, or anything else. Unless I believe in God, I cannot believe in thought: so I can never use thought to disbelieve in God.
C.S.Lewis: The Case for Christianity
It is hard to believe he thought this through but perhaps he had just got carried away with his early success and was taking his target audience too much for granted and getting careless.
Of course, even if we share Lewis's genuine ignorance of neurophysiology and feigned ignorance of evolution, and accept for the sake of argument that thinking is a random process, it is unavoidable to any honest thinking person that the same logic applies equally to his argument leading to belief in a god as to arguments leading to Atheism.
Lewis has too obviously betrayed his double standards and ability to compartmentalise his thinking, using one standard for arguments against Atheism and a much lower standard for arguments leading to belief in gods.
He had apparently tried out various versions of this piece of sophistry:
...but did not distinguish between physical causes of beliefs and rational grounds for belief. He also claimed atomic motions in the brain are 'irrational'.
In a Socratic Club debate, G.E.M. Anscombe criticized this, accusing him of taking advantage of ambiguous meanings of the words "why", "because", and "explanation", which prompted Lewis to revise the chapter. The revised chapter presents a more detailed elucidation of the argument, distinguishing clearly between the causes of beliefs and the grounds of beliefs, and also changing most uses of "irrational" to "non-rational".
According to George Sayer, Lewis's friend and biographer, Lewis regarded the debate as a defeat, and felt humiliated by it:
He told me that he had been proved wrong, and that his argument for the existence of God had been demolished. ...The debate had been a humiliating experience, but perhaps it was ultimately good for him. In the past, he had been too proud of his logical ability. Now he was humbled ....'I can never write another book of that sort' he said to me of Miracles. And he never did. He also never wrote another theological book.
Source: Wikipedia - Argument From Reason
So, it seems that even C.S.Lewis realised he had gone too far with that one. Quite clearly, whatever god Lewis professed to believe in, it was at best, a God of Low Standards.