In a small bowl, whisk together the vinegar, 2 teaspoons of the oil, and the sugar. Add mint and stir to combine. Season with 1/2 teaspoon salt and pepper to taste and set aside.
Heat a skillet over medium-high heat, and add the remaining olive oil.
Season lamb with salt and pepper. Working in batches, cook chops in skillet until medium rare, about 2 minutes per side. Transfer to a cutting board and tent with foil. Let rest 5 minutes.
Top with the mint mixture and serve immediately.