“Justice means much more than the sort of thing that goes on in law courts,” C. S. Lewis would remind listeners in a famous lecture series. “It is the old name for everything we should now call ‘fairness’; it includes honesty, give and take, truthfulness, keeping promises, and all that side of life.”
This is why Justice is “the right thing to do” - there no word for it. But this American expression captures it the best way