Combine apricots and lemon rind and juice in container of an electric blender; process until smooth. Set aside.
Bring water to a boil in a large saucepan; add sugar, and boil 1 minute. Remove from heat, and cool completely. Add flavorings.
Pour water mixture and apricot mixture into freezer can of a 2-quart hand-turned or electric freezer. Freeze according to manufacturer's instructions 5 minutes or until mixture thickens.
Beat egg whites (at room temperature) until stiff peaks form; fold into whipped cream. Fold whipped cream mixture into apricot mixture. Continue to freeze according to manufacturer's instructions. Let ripen at least 1 hour before serving. Scoop into sherbet dishes, and serve immediately.