I don’t have access to a history of Sicily and was curious if the name predated the Crusades or if it was named for him.
The Encyclopedia Britannica article on the town of Corleone notes that “the name Qurliyun is found in Arab sources of the 9th century AD”. It’s not totally clear if (as I assume) “Qurliyun” is an Arab rendering of a Latin/Italian name meaning “heart of the lion”, or if Corleone/Cuor di Leone is a folk etymology “explanation” of an Arab name “Qurliyun” with some other meaning. Either way, since Richard the Lion-hearted lived 1157-1199, the answer to the question would appear to be no.
The usage of the term “lion-hearted” to denote courage goes back to the time when Og the Timid first saw a lion and coined the term to describe himself (since, in fact, Og was not really an imposing figure). Og invented “spin doctoring” by thereafter referring to himself as “The heart of a lion in the body of a warthog” but he was still unsuccessful in attracting a girlfriend. 
Richard (the King) was given the nickname “lion heart”, but he was not the first to be tagged in this fashion, just the best known. I’m confident that the citizens of Qurliyun, in an effort to improve their municipal image, were quick to see the advantages of being deemed brave and courageous and adopted the Corleone name.