In a large bowl combine the marinade ingredients. Add the lamb to the bowl and evenly coat the meat with the marinade on all sides. Cover the bowl and refrigerate for about 8 hours.
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While the lamb is marinating, make the salad. Cut each tomato lengthwise in half. Cut each cucumber lengthwise into quarters and then cut the quarters crosswise into 12-millimeter pieces. In a medium bowl combine all of the salad ingredients, including ½ teaspoon salt, and mix well. Set aside at room temperature until ready to serve.
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Remove the lamb from the bowl and wipe off the excess marinade, leaving a thin coating. Season the lamb evenly with 2 teaspoons salt. Allow the lamb to stand at room temperature for 30 minutes before grilling.
Prepare the grill for indirect cooking over medium heat (180° to 230°C).
Brush the cooking grates clean. Sear the lamb over direct heat, with the lid closed, until nicely browned on both sides, 10 to 15 minutes, turning once or twice. Slide the lamb over indirect medium heat, close the lid, and continue cooking to your desired doneness, about 20 minutes for medium rare. Remove from the grill and let rest for about 10 minutes.
Cut the lamb across the grain into 6-millimeter slices. Serve warm with the salad.