Jesus is the King of Righteousness! I think one of the ways to interpret the idea that He is the King of Righteousness is because He specializes in it!

What do you call someone when they are the best at rock?
Elvis, the King of rock.

What do you call someone when they are the best at golf?
Tiger, the King of golf.

The "king" is the best, at what he does!

So when the Lord Jesus finds someone like me, whose righteousness is like filthy rags, and doesn't break a sweat in making me the very righteousness of God ... what else do you call Him, except the "King of Righteousness?!?!" He transforms filth into purity, and He does this globally to thousands of people - making each of them just as righteous as Himself, with nothing lacking, so that they are equipped to walk in His ways.

Of course, they call Him the "King of Righteousness," the Lord Jesus specializes in Righteousness, and if you lack righteousness of your own, then go to Him in prayer and ask for it ... you won't be disappointed.