I'm American and my first instinct is loo-SEE-uh, and then LOO-sha. I probably wouldn't know to say loo-CHEE-uh unless someone told me.
I know a dog named
Lucia "LOO-sha", named after the saint, and a boy named
Lucian "LOO-shun" as well as a younger boy named
Lucian "LOO-see-an".