I don't know if it is limited to Luck 3, but I believe it is luck 2 (Don't quote me on it).

Kriss cleared up some of the requirements as you can see

The Barbarian Horde is less of an issue to me for the most part, because if it happens to hit your Capital then 99% of the time you will fend it off (The Horde isn't too strong) and not lose too many patrollers. And if it hits a non-production province it's not really that much of an issue to go get it back.

I would like the horde to get stronger as the game progresses Just to tell you how I feel about bad events, the same way I'd like the lucky ones to get stronger (Militia/Flags) to represent some of the power struggle and usefulness/detriment as the game progresses.