Leonora is an Italian variant that arose from Eleanor (#60 in the U.S.), meaning "light." It is pronounced LAY-oh-nor-uh in Spanish and Italian, while it is mainly pronounced leh-NOR-uh in English.
Lenora is a modern English spelling of Leonora, only pronounced leh-NOR-uh. Lenore is the German variant most people will recognize, thanks to Edgar Allan Poe's poems Lenore and The Raven. Also, Gottfried August Burger had a ballad titled "Lenore."
Stats for these names: There were 47 girls named Leonora in 2015, and the name was already in use when the SSA started keeping track of names. Its highest point was 1924 with 138 births that year. There were 130 girls named Lenora, and this name also ranked highest in 1924 with 678 given the name. Lenore, on the other hand, ranked highest a bit later in 1926 with 461 births, stayed in the higher parts of the top 1000 until mid-century, the low parts until the early 1970's, and now is at 67 births in 2015. Leonor was given to 40 girls in 2015 and never saw the numbers the other spellings did. Other seldom-used spelling variants include Lynora, Linora, Lanora, Leanora, Leenora, Lenoria and Lanore.
Elinor, Ellen, Nora, Aliénor, Eleonora, Lore and Norina are also variants of Eleanor. There are dozens of namesakes for all of these spellings and Lenore, Lenora and Leonora.