1. Through intuition, we know that there is an objective morality, which we may call "The Law of Nature."
2. This law is different than other natural laws, such as gravity, in that we may choose whether or not to follow it.
3. Scientific knowledge depends on observable fact--another form of acquisition of knowledge is intuition. It is through the latter we comprehend morality.
4. If there is a reason behind the universe, it cannot in itself be a fact of the universe: it must be external to it. And, being external to the universe, it is thus unobservable through fact-gathering methods--thus science is of no use in looking for such a reason.
5. If there were an external controlling power to the universe, a deity, "[t]he only way we in which we could expect it to show itself would be inside ourselves as an influence or a command trying to get us to behave in a certain way."
6. As per number 1, we indeed find such a command.
7. Therefore, our evidence suggests the existence of a god.
My response to step 2:
While true that physical laws do seem to differ from moral laws, we can reformulate a moral law to be as inviolable as a physical law. Consider rephrasing "Thou shalt not murder" (assume the truth of this command for argument) as "You may not rightly murder." Such a law cannot be violated--it is impossible to murder and be in the right, just as surely as it is impossible to defy gravity and other physical laws.
My response to step 3:
Much depends on Lewis' characterization of morality as being sensible by a altogether different faculty than fact. If morality were simply another external fact to be observed, then by Lewis's own argument, it could no more convey to us meaning about God than any of our other senses could (step 4 & 5).
I, however, think morality is perceived by a similar faculty as fact. Light flashes--I take this in through some sense and, based on it, judge an object to be in front of me. A moral situation presents itself--I take this in through some sense and, based on it, judge rightness or wrongness to obtain.
A weakness in my response:
There is a difference in kind between morality and vision. I know how my eyes work (roughly)--I do not know how I am able to perceive morality. If I have no way of so perceiving, no evident sense, and yet the belief that such morality exists persists, then there are few other explanations for the sensation than some kind of "intuition" of the kind Lewis is arguing for.
In my defense, Aristotle didn't know how his eyes worked, and yet he trusted them as reliable tools for acquiring external fact, and was justified in doing so. Maybe moral epistemology will be cleared up in the future.
My response to step 5:
This seems unfounded. A god could just as easily reveal himself through a message, grasped by intuition, flashing "I am real" or some such. But, which is probably more problematic, Lewis seems to have robbed his god of any ability to influence the material world in an observable fashion. It is hard to see why such a restriction should hold.
To use one of Lewis's metaphors, if the architect must indeed be external to the house as a god must be external to the universe, it does not follow that the architect is unable to make his presence known in the house--he could autograph a brick somewhere. It is unclear why God would not be able to communicate in a similar fashion--even if he is beyond his creation by necessity.
If God could make himself known through all channels, fact and intuition alike, then even granting the existence of morality as evidence in his favor, we must also count the lack of evidence in the observable world as evidence against his existence. And it seems to me that the dearth should weigh significantly more.
UPDATE: Zach, below, has questioned my representation of Lewis's God as being unable to influence the world in an observable manner. I admit that this is flatly contradicted by other things Lewis admits to believing, but I know of no other way to read this passage: "If there was a controlling power outside the universe, it could not show itself as one of the facts inside the universe--no more than an architect of a house could actually be a wall or staircase or fireplace in that house."