Preheat oven to 250°F. Mix flour, 3/4 teaspoon coarse salt, and 1/2 teaspoon ground pepper on large plate. Lightly coat lamb chops with flour mixture; shake off excess. Melt butter with oil in large nonstick skillet over medium-high heat. Add lamb chops and cook to desired doneness, about 3 minutes per side for medium-rare. Transfer chops to baking sheet and keep warm in oven while preparing sauce (do not clean skillet).
Add onion to same skillet and sauté 2 minutes. Add cherry juice and bring to boil, scraping up any browned bits. Boil until liquid is slightly reduced and onion is slightly softened, stirring frequently, about 4 minutes. Stir in cherries and half of basil and cook 1 minute. Season sauce to taste with salt and pepper.
Place 2 lamb chops on each of 4 plates. Spoon sauce over. Sprinkle remaining basil over and serve.