In a blender, whirl yellow onion, garlic, rosemary, lemon juice, and salt. With blender running, slowly pour in olive oil.
Rinse lamb and pat dry. With a small knife, make small slashes (1 in. long, 1 in. deep) all over the lamb, and put it in a nonreactive dish. Coat lamb with onion marinade, making sure the mixture gets into the slits. Cover and chill 2 hours or up to overnight, turning occasionally.
Remove lamb from refrigerator about 1 hour before you plan to cook it. Spread lamb flat on an oiled barbecue grill over a solid bed of medium-hot coals or medium heat on a gas grill (you can hold your hand 1 to 2 in. above grill level only 4 to 5 seconds). Close lid. Cook lamb, turning once and brushing with marinade, until a thermometer inserted in center of thickest part registers 140°, about 40 minutes.
Transfer meat to a platter and cover. Let rest 15 to 20 minutes. Thinly slice meat, garnish with sliced red onion and radishes, and serve with yogurt-mint sauce.
Note: Nutritional analysis is per serving.
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