In Mere Christianity, C.S. Lewis bases his idea of what he calls the Law or Rule about Right and Wrong upon the idea that there is a universal understanding of a Law of Human Nature. He says this is proved by (1) the similarity between what humans admire or blame (e.g., admire promises kept; blame selfishness) and (2) how many excuses people find for themselves when they don't follow the Law of Human Nature.
Lewis further says it is not disproved by (1) the differences in moral conduct between cultures (e.g., one wife or four; slavery for enemies in ancient times or no slavery in current times) because within these variations there is still the instinctive or natural response to know how a person "ought" to behave. He also says it is not disproved by (2) the fact that people habitually do not live according to what they know they ought to do since when they do not do as they ought, they make up strings of excuses for why on that occasion and in that instance it was understandable that they should break the Law of Human Nature.
Based on this summary of Lewis's ideas on Right and Wrong in Mere Christianity, according to Lewis it is right to practice ourselves the kind of behavior we expect from others. This is true, according to Lewis, because what we expect from others is the same as what we know we ought to do ourselves in accord with the Law of Human Nature.
Having said this, Lewis makes it clear that humanity in all ages and the world over in major and minor cultures--Westernized, civilized, or indigenous--habitually breaks this Law of Human Nature. Lewis says: "First, that human beings, all over the earth, have this curious idea that they ought to behave in a certain way, and cannot really get rid of it. Secondly, that they do not in fact behave in that way. They know the Law of Nature; they break it. These two facts are the foundation of all clear thinking about ourselves and the universe we live in" (C.S. Lewis, Mere Christianity).
There are a couple of issues going on here. The first is the premise from which Lewis operates. His read of how people should act is driven from a sacred point of view, in this case, Christianity. While there is nothing wrong with having this as a foundation, it is limiting in that most religious premises have a tendency to view themselves in spiritually absolute terms. This means, essentially, that the Christian point of view becomes the dominant one in this paradigm. There are billions of people out there that might disagree with such a view. This might be the first issue to be raised. The second issue might be more philosophical in nature. The concept has some fundamental concerns with it in that it places most of the power in the hands of one individual: The person charged with the duty of empathy. In the link below, the question is brilliantly asked that instead of presuming what someone else would want us to do to them, why not simply ask them their opinion? The idea of "do unto others" places decision making in the hands of one individual and fails to integrate a collective solution to problems because it neglects to take the other side into account. In a more abstract way, what happens if the individual cannot envision or lacks the moral empathetic skills to understand how the other would want to feel? It seems that placing all the power in the hands of one person- the one that is supposed to ask what others would expect- does not work if they lack the moral fiber or character to make such a decision. How else could one explain why suicide bombers do what they do or why random acts of violence happen? Certainly, Dylan Klebold and Eric Harris lacked the moral understanding or capacity to place themselves in another's shoes, as they taunted many of their victims before killing them. Another challenge with the Golden Rule would be that it only seeks to make moral equivalency and lacks any real criteria for establishing what is appropriate conduct. Presumably, two mass murderers could reach moral agreement under the Golden Rule. This makes the idea of using ourselves as the sole basis for making moral calculations a challenging one. Certainly, our interpretation should be a part of this decision making process, but validating the voice and experience of "the other" might also be an effective inclusion in determining what the right thing to do is.
Well, as CS Lewis was a Christian, he certainly condones the Biblical direction to "Do unto others as you would have them do unto you." (Luke 3:61, New Testament.)
In everything he's written, CS Lewis generally teaches the principles of humility, servanthood, putting others first, etc. In that simple philosophy, it is pretty clear that he believes it would be wrong not to practice the kind of behavior we expect from others. In fact, he would also agree that people "reap what they sow." If you sow goodness and kindness, you will in turn receive goodness and kindness. On the flip side, if you sow destruction, you will reap destruction.