Preparation Prepare a gas grill for direct-heat cooking over moderately high heat. Cut 8 thin slices from lemons, then squeeze enough juice from remainder to measure 2 tablespoons and put in a bowl. Halve cheese diagonally, then cut each triangle, cut side down, into 1/3-inch-thick slices. Mince garlic and mash to a paste with a pinch of salt using side of a large heavy knife, then add to lemon juice. Whisk in salt and sugar until dissolved, then add 1/4 cup oil, whisking until combined. Separately toss lemon slices and cheese each with 1/2 tablespoon dressing. Brush both sides of bread with remaining 2 tablespoons oil. 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 (2 to 3 minutes total), grill marks appear on cheese (3 to 4 minutes total), and lemons begin to wilt (4 to 6 minutes total). Whisk dill into remaining dressing. Divide bread among 4 small 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.