Who was Lucy Gray?

This question is a little confusing, as the character Lucy Gray does not appear in Wordsworth's "Composed Upon Westminster Bridge." "Westminster Bridge" is a sonnet—a lyrical work expressing an emotion—about how lovely the city of London is in its peaceful, early dawn state, before the noise, bustle, and confusion of the day begins.
"Lucy Gray," however, is a different Wordsworth poem. It is a ballad, or narrative poem, about a little girl (Lucy Gray) who is sent to fetch her mother during a snowstorm and gets lost. Her parents trace her footsteps in the snow to a bridge, where she presumably fell off. However, some people report seeing her ghost among the hills and valleys of the Lake District. She was a child who embodied nature and loved to play outside, and perhaps her spirit still gambols among the plants and animals of the natural world.
Both poems, though different, celebrate and exhibit a love for nature. "Westminster Bridge" expresses the speaker's wonder that a city—usually associated by Wordsworth with corruption and depicted as the antithesis of nature—can have such a peaceful, natural beauty in the early morning, and "Lucy Gray" depicts a young girl as a beautiful and innocent child of nature.