1. Heat oil in a large nonstick skillet over medium heat. Add onion and sugar to pan; cook 10 minutes, stirring frequently. Stir in 1/8 teaspoon salt. Reduce heat; cook 8 minutes or until tender and browned, stirring occasionally. Keep warm.
2. Preheat broiler.
3. Combine remaining 1/4 teaspoon salt, pepper, and lamb in a large bowl. Divide lamb mixture into 8 equal portions; shape each into a 1/2-inch-thick patty. Place patties on the rack of a broiler pan coated with cooking spray; place rack in pan. Broil 6 minutes, turning once after 3 minutes. Remove from oven; let stand 3 minutes.
4. Broil buns, cut sides up, 2 minutes or until lightly toasted. Place patties on bottom halves of buns; top each patty with about 1 1/2 tablespoons caramelized onion and about 3/4 teaspoon blue cheese. Cover with top halves of buns.