This argument did not originate with CS Lewis, but he popularised it in his 1952 book Mere Christianity, and it has been widely used by Evangelical apologists ever since. The argument runs something like this: Jesus made a number of quite startling claims about himself, like "the Father and I are one", or "no-one comes to the Father but through me". In the light of these claims, it is not reasonable to suggest that Jesus was merely a good man or an inspired teacher. If he made these claims believing them to be true, but they were not, he was a lunatic with delusions of gradeur. If he made them knowing they were not true, he was simply a charlatan. If he was neither of these things, then we are forced to acknowledge his lordship and submit to him.
Apologetics serves two purposes. It bolsters the faith of those who may be questioning or wavering, and it entices and convinces those who are open and enquiring towards the faith. The "liar, lunatic or Lord" argument has been successful on both counts. For Evangelicals it serves as a bulwark not so much against outright unbelief as against more liberal or progessive forms of Christianity, suggesting that these theologies are unreasonable. For inquirers from outside, it is a psychologically astute strategy because it plays on a point of sympathy. In our society organised religion attracts a good deal of suspicion but Jesus himself tends to be viewed a lot more sympathetically. Many who think this way actually know very little about Jesus, and this argument encourages them to take a closer look.
It's a pity the argument doesn't stand up very well to scrutiny. The main source of its weakness is that it enters the question at the half-way point, assuming things it is not safe to assume.
Anyone familiar with the accounts of Jesus' life contained in the Gospels, from fundamentalist Christians to wholly secular scholars, agrees that they were not written by Jesus. They were written by various of his early followers, no earlier than 30 years after the events they describe and in some instances possibly as many as 70 years after.
There are then two basic possibilities - they are accurate factual accounts of Jesus' words and deeds, or they are not. These two possibilities and their various sub-sets are the subject of fierce dispute amongst New Testament scholars and in the wider church.
If they are factual accounts, then Lewis' argument holds. If they are not a range of other possibilities opens up. These possibilities focus not so much on Jesus himself as on the disciples and their motivations. Here are three.
It is possible that they were secretive. On this interpretation, the Gospel writers regarded the real truth about Jesus as something to be revealed only to a select few, either because the knowledge was politically sensitive or because early Christianity functioned as a mystery religion with outer and inner circles. The gospels are a smokescreen, presenting Jesus for popular consumption while embedding the deeper truth in a code revealed only to initiates. The fact there is little evidence to support this idea doesn't prevent a substantial number of people from believing it.
A second possibility is that they were simply mistaken. In the time that elapsed between the events of Jesus' life and the writing of the gospels, the stories grew and changed in the retelling. The gospels, in this view, record this inflated story, which is at some remove from the original events. Some scholars believe it is impossible to get behind this version to the "real" truth of Jesus, while others expend great effort and time in the attempt. The result of their labours is generally some version of the very position Lewis was trying to debunk - Jesus was a good man, gifted teacher, etc but not divine. The key weakness of this view can be seen by asking the question - why were the originals of these stories circulating in the first place?
Finally, it is possible that they have been misunderstood. The cultural distance between us and them means that we are disposed to take the accounts literally in the way Lewis does. The original writers, in this explanation, intended them to be understood symbolically, drawing on images from the Old Testament and Roman culture to present an alternative view of Jewish spirituality and the imperatives of empire. Of course the actuality behind the symbols still needs to be identified and understood in this interpretation.
I know I bang on a lot about bad apologetics. The risk is that when people discover the logical faults in the arguments that support their faith, they abandon the entire faith, not just the bits based on the faulty arguments. We set believers up for a fall.
I'm not entirely sure what a good apologetic is on this, but I suspect it begins with the existence of the Gospels themselves. In the face of persecution by the Roman authorities, ostracism from the main stream of Jewish religion and scorn from the leading philosophers of the age, the first generation of Christians had sufficient reverence for Jesus to sustain their faith, pass it on to a second generation and record it for posterity. Whatever the precise nature of the records, their history is enough to make us look more closely.
*You can read further thoughts about Lewis' Trilemma here.