Prep: 1. Prepare a gas grill for direct-heat cooking over moderately high heat. 2. Cut 8 thin slices from lemons, then squeeze enough juice from remainder to measure 2 tablespoons and put in a bowl. 3. Halve cheese diagonally, then cut each triangle, cut side down, into 1/3-inch-thick slices. 4. Mince garlic and mash to a paste with a pinch of salt, then add to lemon juice. 5. Whisk in salt and sugar until dissolved, then add 1/4 cup oil, whisking until combined. 6. Separately toss lemon slices and cheese each with 1/2 tablespoon dressing. 7. Brush both sides of bread with remaining 2 tablespoons oil. Make: 1. Grill bread, cheese, and lemon slices on grill rack, covered, turning over once (use a metal spatula to scrape under cheese to loosen before turning), until bread is toasted, grill marks appear on cheese, and lemons begin to wilt (4-6 minutes total). 2. Whisk dill into remaining dressing. Divide bread among 4 plates and top with cheese and lemon slices. Drizzle with dressing and serve immediately. Cooks' note: If you aren't able to grill outdoors, bread, lemon, and cheese can be cooked in a hot oiled well-seasoned large (2-burner) ridged grill pan over moderate heat.