Why does Lucy have faith, examples?

Lucy has faith because she stops to see the good in others... she gives them the benefit of the doubt.

“Well,” said Lucy rather slowly (for she wanted to be truthful and yet not be too hard on him), “well, that was pretty bad. But you’re so sorry for it that I’m sure you will never do it again.”

Even when Lucy doubts herself, she refuses to give in... she has faith.

Lucy went to the room where the wardrobe was. She did not mean to hide in the wardrobe, because she knew that would only set the others talking again about the whole wretched business. But she did want to have one more look inside it; for by this time she was beginning to wonder herself whether Narnia and the Faun had not been a dream.