It should be publicly-funded, like infrastructure. Having a video sharing platform is clearly very important, but I don't think there are any companies that are both capable of running it and trustworthy enough to do so.
I think it'll be the recent past, showing how Lumiose came to be what it is in X/Y. A prequel story could do wonders for X/Y, fleshing out Lysandre with an actual backstory could make him interesting.