I mean, the line doesn't make much sense at all. There is absolutely no reason for her to say that. There are two options for the dating, either they met and started dating or it is some kind of arranged marriage style shit. Both of these are realistically possible in the world they are in.
Now if they had naturally met and started dating they would have talked before, so her saying they have never talked doesn't make much sense. Furthermore it doesn't make much sense for her to say "supposed" in that sentence.
This implies some sort of arranged thing going on. However that doesn't make sense either. Ezreal is a nobody for the most part. His parents are an unknown, and so far as the world and Ezreal know they are dead. This leaves his uncle to arrange it. However his uncle doesn't really like Ezreal and Ezreal no longer has much to do with his uncle. As such his uncle isn't in a position to arrange anything like that, and has no incentive to in the first place. The only time something like that would have been arranged would have been before Ezreal left. There is no reason for the crownguards to arrange anything between Lux and a random kid who is a known troublemaker and has nothing going for him.
It wasn't until after he left that he gained his magical gauntlet, and at that point there is no one in a position to arrange anything. In fact it makes anything arranged less likely due to Demacia's dislike of magic. I highly doubt they would want to bring more magic users into their land, much less put two of them together.
There really isn't a logical reason for them to be dating outside of a natural meeting, and Lux's quote heavily weighs against that possibility. As such I think we can call this an example of a Rioter pulling our legs rather than a realistic impression of the world. If we took jokes/taunts as realistic then Azir apparently likes to pretend to be a pigeon, which doesn't fit with his character at all.
Therefore I declare all in game interactions to be null and void in terms of lore, especially as the League doesn't actually exist anymore so far as I am aware and the Champions are not actually fighting each other. League is a theoretic battle in carefully controlled circumstances using characters from an alternate universe. As such how they act in League is not indicative of how they act in Runeterra.