Lux is the Latin word for light and Satan's original name was Lucifer which means "light bringer." In Genesis God says that there will be strife between Satan's seed and God's seed. So the descendants of Lux referenced in the movie are the fallen angels who followed Satan and the children of disobedience.
The sign above the giant of despair's castle reads "Regnum Tenebris" which is Latin for"the kingdom of darkness."
The original name of the planet Venus was Lucifer which means "giver of light", not the original name of Satan. Satan's original name in unknown, he's just known as "the fallen angel". Modern scholarship generally translates the term in the relevant Bible passage where the Ancient Greek figure's name was historically used (Isaiah 14:12) as "morning star" or "shining one" rather than as a proper noun, Lucifer. Anton LaVey and Leo Taxil have distorted the meaning of the word Lucifer for their own self interests.