Can someone who is not a Christian lead a good life? Maybe a better question to start with would be, can a non-christian do a good work at all? Before this question can be answered, a definition of good needs to be given. If you say that for something to be good, the right motives have to be behind that act, then a non-christian would not be able to do a good work. Although, I know a lot of Christians that would not be able to either. So, maybe I am wrong, but I would say that God takes the works of non-Christians and Christians alike that have poor motives and uses them for good and for the advancement of His Kingdom. Motives aside, it is the common grace of God that allows us to do good works in the first place.
C.S. Lewis's argument is that if you have two people that want to do good works, the one that is more informed on the moral law will have a better idea of what to do. So, can a non-Christian do good works, I suppose. But, as someone said in class, by asking the question you admit that Christianity has in some way an advantage when it comes to good works. So trying to live a good life without being a Christian is like purposefully crippling yourself.
The last points that C.S. Lewis gives a great final answer to this question. First, no one can live a perfect or good life. We have all fallen short and therefore need that saving grace of God. Secondly, the end goal of our lives is not to live a good life. Not to say that good works should not be done. But, the chief end of man is to glorify God and enjoy Him forever. If that is your goal in life then it is my belief that good works will come along with it.