Pat the lamb chops dry and place them in a shallow dish. In a small bowl, stir together 2 tablespoons olive oil, lemon juice, 2 minced garlic cloves, oregano, salt, and pepper. Rub the mixture over both sides of the chops and let them sit at room temperature for 10 minutes.

Heat the remaining tablespoon of olive oil in a large skillet over medium-high heat. Add the lamb chops and cook 3 to 4 minutes per side until browned and cooked to your preferred doneness. Remove the chops to a plate and let them rest for 5 minutes.

While the lamb rests, make the tzatziki. In a medium bowl, combine the Greek yogurt, grated cucumber, remaining minced garlic clove, and chopped dill. Stir until smooth and season with a pinch of salt if needed.

Divide the arugula among four plates. Place two lamb chops on each bed of greens and spoon tzatziki over the top or serve it on the side.