Well, since Fai and Lux more or less grew up together because of the whole supposed to get married to each other thing, I would assume that him and Garen having met each other fairly frequently is inevitable. And since he's a huge weirdo who doesn't quite get how to high society despite his fancy family, occasionally acts scandalously, and has been known to hang out in less reputable parts of town... Garen might've found himself wondering if he's such a good match for his precious baby sister.

And now that Lux and Fai both were like NOPE SRY NOT GOING TO GET MARRIED... well, the situation is probably just a bit weird and awkward ^^;;