What are the major themes of C.S. Lewis' Cosmic Trilogy, and do they connect with themes in The Chronicles of Narnia?

Sounds like a homework question to me.

The one thing that definitely connects Lewis's two series is that they are both full of religious allegory and themes. The religious undertones are even more pronounced in the Space Trilogy than in the Chronicles of Narnia; they are hardly undertones anymore.

Read them and find out.

You'll be doing yourself a favour. They are all excellent, vivid stories.

You already picked a best answer, but I want to ring in on this one.  Both sets of stories are based on the idea that morality is universal, i.e. it permeates the universe, so it's the same in foreign lands and on foreign planets--Mars, Venus and Narnia.  Right is right, good is good, bad is bad, even in the farthest reaches of the universe.

It's about 'Christian' principles only because (some) Christians believe morality is exclusively a property of Christianity.  Lewis himself said the Narnia books were an attempt to show Christian morality but not Christianity himself.  But he was just as successful in proving that morality is not necessarily Christian, that what is right and true and good and fair goes beyond Christian philosophy, that Christians didn't invent it.

This is similar to what Isaac Newton discovered about the universe.  By showing that the planets orbit the sun because of gravity, the same gravity we have on earth, he showed that natural laws were truly universal, that gravity, momentum, inertia, time, space, mass, etc. were the same everywhere.  Believe it or not, this came as a great shock at the time.