The words lux, luxe sound the same but have different meanings and spellings. Why do lux, luxe sound the same even though they are completely different words?
The answer is simple: lux, luxe are homophones of the English language.
The International System unit of illumination, equal to one lumen per square meter. See Table at measurement.
The condition of being elegantly sumptuous.
Something luxurious; a luxury.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.