As pointed out in other answers, it's not good Latin. I assume (I hope!) it was not meant to be, either.
In my interpretation the "ex" is just the English word, so the name "Ex Lux" means "Former Lux". This is similar to how "ex-girlfriend" means "former girlfriend".
However, I believe the allusion to Latin is fully intentional. The original name "Lux" is indeed a Latin word — and lux is what a lucifer carries. I assume "ex" also has its origin in Latin, but I don't think the two words try to mean anything together in Latin. The two words have a Latin origin by they were put together in English, not in Latin.
The name looks better to me without a hyphen. This spelling variant also gives a more Latinate feel to it. Business names and proper spelling don't always go together, unfortunately.