Luxio shares the same name in all languages: Luxio. According to Bulbagarden, Luxio comes from a combination of the Latin word for light: Lux and a corruption of Leo. They also mention Luxor, a city where the Egyptian temple of Karnak resides, has an avenue of Sphinxes. This could probably be due to its pre-evolution "Shinx" and how its name sounds similar to Sphinx. However, Luxio does not share more obvious traits with Sphinxes, so I feel that mentioning Luxor is misleading. Luxor's name actually comes from the arabic name al-Uqsur meaning: "the palaces".
Lux, from the latin for light, makes far more sense. Lux could also be a reference to the SI unit of measuring luminous flux. Meaning: the measurement of light that is seen off of a surface by the human eye. Luxio is known as the Spark Pokemon and emits bursts of light.
"-io" undeniably comes from Leo, the latin name for Lion. A combination of both Latin words would make sense for Luxio's name origin, and also for how it remains unchanging through many different languages.