According to the C. S. Lewis website, this is one of the quotes frequently misattributed to Lewis. It actually appeared in a book by Charles Marshall called Shattering the Glass Slipper.

However, in Mere Christianity, chapter 3, book 2, Lewis said something along the same lines:

We might think that, provided you did the right thing, it did not matter how or why you did it—whether you did it willingly or unwillingly, sulkily or cheerfully, through fear of public opinion or for its own sake. But the truth is that right actions done for the wrong reason do not help to build the internal quality or character called a "virtue", and it is this quality or character that really matters.

Both quotes are saying roughly the same thing: that integrity—which Lewis calls "character"—comes from within. It is a habitual response that becomes so ingrained that it is what a person does automatically. Integrity becomes a reflex, simply a part of who a person is.

Both writers are trying to impress on readers that integrity or character requires an inward transformation. True integrity is not what we do because we wish to earn a reward or because we fear punishment.

Throughout Mere Christianity, Lewis is trying, in simple terms, to help ordinary people understand Christian theology in an everyday way. He goes to pains to emphasize character as deeper than good public behavior, because that point was integral to Jesus's teaching in the gospels. Jesus told stories to condemn people who prayed loudly to earn public acclaim, and, instead, Jesus argued that good deeds should be done quietly.

Lewis is attempting to emphasize that Christianity is a matter of changing one's heart and outlook, not one's outward behavior. It means wanting to do the right thing because it is the right thing.