On the possibility of a cumulative case, see Peterson, Reason and Religious Belief, 115–6.
What Peterson ignores is Lewis's chapter 9, "Animal Pain," where he writes:
"It seems to me, therefore, a reasonable supposition, that some mighty created power had already been at work for ill on the material universe, or the solar system, or at least, the planet Earth, before ever man came on the scene: and that when man fell, someone had, indeed, tempted him. This hypothesis is not introduced as a general "explanation of evil": it only gives a wider application to the principle that evil comes from the abuse of free will. If there is such a power, as I myself believe, it may well have corrupted the animal creation before man appeared. The intrinsic evil of the animal world lies in the fact that animals, or some animals, live by destroying each other. That plants do the same I will not admit to be an evil. The Satanic corruption of the beasts would therefore be analogous, in one respect, to the Satanic corruption of man. For one result of man's fall was that his animality fell back from the humanity into which it had been taken up but which could no longer rule it. In the same way, animality may have been encouraged to slip back into behaviour proper to vegetables. It is, of course, true that the immense mortality occasioned by the fact that many beasts live on beasts is balanced, in nature, by an immense birth-rate, and it might seem, that if all animals had been herbivorous and healthy, they would mostly starve as a result of their own multiplication. But I take the fecundity and the death-rate to be correlative phenomena. There was, perhaps, no necessity for such an excess of the sexual impulse: the Lord of this world thought of it as a response to carnivorousness -- a double scheme for securing the maximum amount of torture. It it offends less, you may say that the 'life-force' is corrupted, where I say that living creatures were corrupted by an evil angelic being. We mean the same thing: but I find it easier to believe in a myth of gods and demons than in one of hypostatised abstract nouns. And after all, our mythology may be much nearer to literal truth than we suppose. Let us not forget that Our Lord, on one occasion, attributes human disease not to God's wrath, nor to nature, but quite explicitly to Satan. [Luke 13:16]
If this hypothesis is worth considering, it is also worth considering whether man, at his first coming into the world, had not already a redemptive function to perform. Man, even now, can do wonders to animals: my cat and dog live together in my house and seem to like it. It may have been one of man's functions to restore peace to the animal world, and if he had not joined the enemy he might have succeeded in doing so to an extant now hardly imaginable."
So should there be good evidence for ID, then Lewis would not have been troubled that there might also be evidence for evil ID. For him, Satan would be a prime candidate for the role.