These are three superb books that are helpful for the thinking non-Christian who is open to exploring the gospel more.
Letters From a Skeptic
This book includes the actual letters between Gregory Boyd and his non-Christian father. It includes so many questions about the Christian faith. A highly readable book. Superb.
The Reason for God
Tim Keller is one of our brightest pastors today. This is an excellent book to give to the thinking non-Christian. Great for us who are believers too.
During World War II the BBC asked Lewis to make a series of broadcasts about Christianity. These broadcasts were later compiled into the book Mere Christianity. Perhaps the most influential Christian book of the 20th century. Brief, but powerful. Lewis could write.