1. In a small bowl combine the aioli ingredients. Set aside.
2. Coat the lamb on all sides with the oil and season evenly with the salt and pepper. Allow the lamb to stand at room temperature for 15 to 30 minutes before grilling.
3. Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F).
4. Brush the cooking grates clean. Sear the lamb over direct medium heat, with the lid closed as much as possible, until nicely browned on both sides, 10 to 15 minutes, turning once. Slide the lamb over indirect medium heat and cook, with the lid closed, to your desired doneness, 20 to 30 minutes for medium rare. Remove from the grill and let rest for 5 to 10 minutes.
5. Cut the lamb crosswise into 1/4-inch slices. Serve warm with the aioli.