How does C.S Lewis come to the conclusion that Jesus is God?

why do we come to say that he is God simply like that if he could also be a lunatic or something worse? 

Lewis, at this point in the book, is arguing against a specific view of Jesus - namely that he was a wise man, a good man, a great teacher - but not God! It's a widely held view among people who haven't looked closely at the Gospels, and it's a convenient one for people who want to acknowledge Jesus as an ideal, but either don't want to accept the supernatural or acknowledge Jesus as their Lord . So Lewis isn't looking to refute the "lunatic" or "fiend" viewpoints in that section. Neither is he looking to produce a "mathematical" proof.

So the point of the section of the book is that only three views of Jesus are reasonable. Which one you choose is left to other parts of the book, and the reader's own investigations.

As he says:

It seems to me obvious that he is neither a lunatic or a fiend.

He has read up about Jesus, both the stories of his life and what others have thought of him, and come to the conclusion that "lunatic" and "devil" are both off the table. Most people, even those who don't believe Jesus is God, would probably agree.

The trilemma is NOT C.S. Lewis's only reason on why he came to the conclusion that Jesus is God (he covered this topic in his other books). I think C.S. Lewis used this logic in Mere Christianity only to refute the false assertion that Jesus was a mere teacher. It was intended as a short summary to brush away a distraction from the main meat of the book: an informal presentation of the Christian faith. It wasn't meant as a rigorous scholarly argument. I think in the passage you cited C.S. Lewis was merely trying to disabuse his listeners in just 1-2 minutes (Mere Christianity was originally a radio talk) of the false argument that Jesus was a mere teacher, so his listeners kept an open mind when reading the gospel accounts, which everyone accepts to be an indispensable extant account into who Jesus was.

If this question focuses on the insufficient details in the trilemma, this is a legitimate assertion; the Wikipedia article on Lewis's Trilemma lists criticisms based on false premises, ambiguous terms, and unsound logical form by credentialed Bible scholars and philosophers.

I myself used to struggle with this, but after 1) I accepted a major unstated premise (that the Gospel accounts are not Legend) and after 2) properly reading the Gospels in the context of the Old Testament, I can accept the Trilemma as "obvious" and reasonable. The Responses section of the same Wikipedia article, also lists some defenders who are also credentialed philosophers.

1. The gospel accounts are not Legend. This means that the Gospels is a trustworthy account by the earliest witnesses.
   • Jesus really said the words printed in red in some Bibles. They don't have to be word for word verbatim (like in a court transcript), but each of Jesus's sayings was reproduced by the gospel author faithfully without corrupting Jesus's original meaning.
   • We have to allow each gospel author's adding a structural/narrative form around the sayings to make additional theological points that also do not corrupt Jesus's original meaning.
2. The gospel accounts need to be read from the point of view of Jews who knew their Scriptures (the OT). This is how C.S. Lewis read the gospels, of course, since he was a literature scholar who obviously knew how to approach ancient literature properly and consequently knew how to bring into the reading necessary contexts, idioms, belief systems, word meanings, etc. assumed by the original audience. In Mere Christianity he implied we would read the gospel accounts similarly, which mean we need to be cognizant of the plethora of OT references and prophecies such as:
   • The significance of Jesus's usage of "The Son of Man"
   • God's fulfillment of the Davidic covenant in Jesus as the everlasting King
   • The precise wording in the saying that implies he exists before Abraham Jesus claimed to be God (which was similar to God's self-identification to Moses in the burning bush)
   • Jesus's claims that he was greater than Moses because he gave "manna from heaven" that doesn't go bad after 1 day, also implied by the 2 miracles of the feeding of thousands
   • a) Jesus's offering "The Sign of Jonah" before his death and b) his resurrection as empirical validation of the sign, proves that Jesus is a true prophet according to the OT logic of validating a prophecy / prophet.
   • The argument that the power of his miracles come from God, not the devil, shows that he was not a devil trying to deceive his audience by tricks
   • The significance of God's affirmation from heaven during his baptism and his transfiguration meant third-party validations of Jesus's claim by authorities already accepted by the audience: God the Father as well as Moses and Elijah (transfiguration)
   • The significance of another prophet John the Baptist's testimony of Jesus as the greater one is another third party testimony.
   • etc.

Armed with the above two points we are now more ready to assess C.S. Lewis's trilemma as Jesus being either Lord, Liar, or Lunatic:

1. Lord: the Gospels properly read by the original audience and deemed trustworthy by the early church clearly made the case that Jesus claimed to be King, Prophet, Priest, Messiah, Judge (at second coming) and God. Someone like this, who also survived death (and defeated Devil) deserved to be a Lord. What's more, God in heaven (God the Father) gave His stamp of approval! If we trust God the Father (like the gospel's original audience) and if we trust that everything described in the Gospel accounts came true, this option is very compelling to reasonable people.
2. Liar: or "fiend" implies the power of his miracles came from the Devil who tries to trick people into committing blasphemy by regarding Jesus as God. The Pharisees argued for this option (false messiah, false prophet, power coming from the Devil) but I think the Gospel account properly read contain sufficient material for us to exclude this option.
3. Lunatic: implies Jesus was deluded or a megalomaniac, and that the early followers were similarly crazy. Many apologists including G.K. Chesterton in his book "Orthodoxy" argue that the Gospel accounts don't present a person (Jesus) who is lunatic.