I realize you can easily get lost in the weeds here with Lewis.
But this raises a significant issue.
Even if you can justify virtue out of determinism – it does not follow that you should act with virtue.
First of all, I don’t think you can justify virtue out of determinism.
For the universe is blind physics without care or want or need.
Ethics does not follow from there.
Therefore, you have the same problem with wanting people to act with virtue.
It would be like arguing on ethical grounds that an ant should not eat an aphid.
But this course, though less inhuman, is not less disastrous than the opposite alternative of cynical propaganda. Let us suppose for a moment that the harder virtues could really be theoretically justified with no appeal to objective value. It still remains true that no justification of virtue will enable a man to be virtuous. Without the aid of trained emotions the intellect is powerless against the animal organism.