Place cucumber in a blender; process until smooth. Place cucumber in a sieve; sprinkle with 1/8 teaspoon salt. Drain 1 hour. Combine cucumber, yogurt, and next 5 ingredients (yogurt through garlic) in a small bowl; stir until well-blended.
Trim fat from lamb; cut into 1-inch cubes. Combine the broth, 1/4 teaspoon salt, and pepper in a medium saucepan. Bring to a boil; cook 2 minutes. Pour into fondue pot; simmer over medium flame. Pierce lamb with skewer; cook in broth mixture until desired degree of doneness is reached. Serve with yogurt sauce.