Trim off bottom 6 inches of lemongrass stalks. Cut enough lemongrass tops crosswise into ½-inch pieces (discard any discolored parts) to measure ⅓ cup. Bring lemongrass pieces, sugar, and ¾ cups water to a boil in a saucepan, stirring until sugar is dissolved, then remove from heat and let steep, partially covered, 20 minutes. Put remaining water in a pitcher. Blend lemongrass mixture in a blender until lemongrass is finely chopped (use caution when blending hot liquids), then pour through a fine-mesh sieve into water in pitcher, discarding solids. Serve over ice.