A monarchy set up to establish the absolute rule of one's lawn. The ruler of the lawnarchy is the owner, who takes the title of "king." The king orders his underlings, usually his own children, to be responsible for upkeeping his lawn. This includes mowing it, edging it, watering it, raking the leaves off it, and making sure it looks better than any of the neighbor's lawns.
Rick's dad, the king of the family's lawnarchy, forced Rick to edge the grass with a scissors.