Why does Lucy never give up?

Lucy doesn't give up because she believes in doing the right thing... she considers others before she considers herself.

“Oh, but we can't, we can't,” said Lucy suddenly; “don't you see? We can't just go home, not after this. It is all on my account that the poor Faun has got into this trouble. He hid me from the Witch and showed me the way back. That's what it means by comforting the Queen's enemies and fraternizing with Humans. We simply must try to rescue him.”