Today, I finally found a one word description for the particular Deanic Devotional Path of The Lady of Light Chantry. That word is Lucienne.
Lucienne, feminine (French), comparable to Lucien, masculine (French)
forms of the (Latin) word lux (genitive lucis) “light”
Lucienne, used as an adjective, refers both to “The Lady of Light” Chantry, the new name, and “St. Luci, Queen of Lights” Cathedral, the old name, for the Deanic Mystical Order which I founded, way back in 2010.
Now, whenever someone asks me the name of the noble tradition which I follow, I can say, Lucienne.