Slice 1/2 of the lemon into thin slices; set aside. Juice remaining 1/2 lemon into a 1 cup measure; add water to equal 1/2 cup. Stir in sugar. Set aside.
In 12-inch nonstick skillet, heat butter over medium-high heat. Sprinkle salmon with salt and pepper; add to skillet. Cook 2 to 3 minutes or until bottom is golden; turn fillets. Add lemon juice mixture. Top with snipped dill and lemon slices. Reduce heat to medium; cover and cook 5 to 6 minutes more or until fish flakes easily when tested with fork.
Meanwhile, in another skillet heat 1 Tbsp. olive oil. Quarter broccoli lengthwise into long spears; add to skillet along with garlic. Cook over medium heat for 8 to 10 minutes, or until crisp-tender, turning often. Serve salmon with broccoli; pour pan juices over salmon. Serve with additional lemon slices and fresh dill. Makes 4 servings.