Leonore and Lenore are two totally different names (with a common origin). Leonore (pronounced 'leh-oh-NOR-eh') is a short form of the German Eleonore.
Lenore is also a short form, but of Eleanor and pronounced 'le-NOR'.
I love them both, but if I had to choose, tonight I'm feeling partial to Leonore. :) However, there are times in which I also love the Spanish form of Eleanor: Leonor.