Melt 1/4 cup butter in a heavy saucepan over low heat. Add flour, salt, and pepper, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add water; cook over medium heat, stirring constantly, until thickened and bubbly.
Gradually stir in lemon juice and remaining butter, beating constantly, until butter is well blended. Add capers, stirring well. Serve sauce warm over baked or broiled pompano.