Even in FE, more than one Arena could be generated.  However, only one Arena quest could be completed per game; as soon as one was done, the others disappeared from the map.  This is probably still the case in LH, though I haven't even seen the Arena yet.

It still works the same way.  Multiple on map, all clear on completion/fail

Maybe they have events around the country - and move around the monsters for the competitor to fight, but you can visit any location.  Kind of like a chain store. <pun maybe intended>

I kinda like the fact that multiple arenas pop for the quest. Makes it into a bit of a race if you want to complete the quest. Since there are multiple arenas, you don't quite know if someone else is tackling it somewhere else on the map.