Stir fresh cherries together with sugar and macerate while browning chops. If using frozen cherries, stir with any juices and sugar and thaw, about 1 1/2 hours.
Pat lamb dry and sprinkle with salt and pepper. Heat 1 tablespoon oil in a 12-inch nonstick skillet over moderately high heat until hot but not smoking, then sauté 4 chops, turning over once, about 6 minutes total for medium-rare. Transfer to a plate and loosely cover with foil. Cook and transfer remaining 4 chops in same manner.
Pour off fat from skillet and add remaining tablespoon oil. Heat until hot but not smoking, then sauté shallot, stirring, until golden brown, about 3 minutes. Add cherries with juices, broth, and vinegar and bring to a boil, stirring occasionally and scraping up brown bits, then reduce heat and simmer 3 minutes. Add salt and pepper to taste, then add butter and 2 tablespoons mint, stirring just until butter is melted.
Spoon sauce over chops and sprinkle with remaining 2 tablespoons mint.