So we did a little bit of snooping about to figure out just what is up with this title. Turns out that Geoffrey Chaucer wrote a "Book of the Lion" as part of his Canterbury Tales way back in the Middle Ages. He opted not to include the story, though, and the "Book of the Lion" was lost. So we have no idea what it was about, though we're confident that The Book of the Lion is a shout-out to Chaucer. Additionally, King Richard was referred to as the Lion. So since Edmund is on the Crusade with King Richard, the title is also a reference to this leader of the Crusades.
Leaving historical facts aside, though, we can also see the title as simply a shout-out to Edmund and his transformation. He is much stronger than he realizes when the book starts, but by the end, he's started to know his own strength. So we might say Edmund is like a lion in his own right, and that the book is all about him coming into his strength. And so it's called The Book of the Lion.