Light a charcoal grill and let burn until coals are glowing red. (Or heat a grill pan on stovetop.) Grill lamb chops 4 to 5 minutes per side for medium-rare. Transfer chops to one side of grill to keep warm.
Pat zucchini dry, then coat with olive oil. Arrange in a single layer on grill. Cook until tender and grill-marked, 1 to 2 minutes per side. Meanwhile, stir together vinegar and sugar.
Remove zucchini and arrange on a large platter. Scatter mint over zucchini, then drizzle with sweetened vinegar. Add a few grinds of pepper and drizzle with extra-virgin olive oil. Tilt dish to distribute seasonings. Place lamb chops on top of zucchini and serve.