What BtN doesn't tell you is that Leonore is a short form of Eleonore which is the German form of Eleanor (or maybe Eleanor is the English version of Eleonore :)). Whilst Leonore has been a long standing short form, Lenore maybe be a more recent American invention owing to Poe for its existence and subsequent popularity. But I have no absolute proof of that, I'll have to do more research. :)
If you'd like to hear how Leonore is pronounced, click on the 'comments' link on the right-hand side and there will be a link that will appear on the following page.