In a small saucepan, cover the lavender flowers with 1/2 cup of the water and bring to a boil. Simmer over moderately high heat for 3 minutes. Cover, remove from the heat and let stand for 20 minutes. Strain and discard the flowers.
In a small saucepan, combine the sugar with the remaining 3 tablespoons of water and bring to a boil over moderate heat, stirring once or twice to dissolve the sugar. Continue to simmer the syrup, undisturbed, until it reaches 280° on a candy thermometer (soft ball stage), about 4 minutes. Slowly and carefully pour in the strained lavender water, stirring constantly over moderate heat until smooth. Let the lavender syrup cool to room temperature, transfer to a small pitcher and serve.
The syrup can be refrigerated for 3 days. Bring to room temperature before serving.