This is not an Asiatic lily as described in the B&D catalog. It is registered as a longiflorum/Asiatic hybrid lily (aka LA lily) in the RHS Lily Register. Unless I find some specific, reliable information showing otherwise, LAs should be mulched in zones colder than Z5.
As for fall care, I cut all of my liliums back to about 3 inches after the leaves have completely died. The little stump serves as a marker for where to look for spring emergence.
I don't know where the "azucena" comes from. This is either a seller's gimmick or we are talking about a whole different plant, not true lilium. If that is the case, then ignore all I have written.