How does Liesel die at the end?

Liesel dies a natural death in Death's presence. She is an old woman.

After Liesel dies, Death walks down the street with her and shows her The Book Thief, which Death has kept all these years. Death says that it read Liesel's book many times. Liesel asks if Death could understand it; Death does not respond. Death wants to ask her how the human race can be "so ugly and so glorious," but does not. Instead Death tells her the "only truth" it "truly knows": "I am haunted by humans."

Yes. She died at the age of 90 according to the movie, but a different age in the book.