Make the pomegranate syrup: Combine pomegranate juice, sugar and lemon juice in a small saucepan. Bring to a boil, stirring to dissolve the sugar. Reduce heat and simmer for one hour, stirring occasionally. The mixture should coat the back of a wooden spoon. Remove from heat and allow to cool to room temperature. It will continue to thicken as it cools.
Pour 1-2 teaspoons of pomegranate syrup into each chilled champagne flute. Add the Prosecco. Stir gently to dissolve the syrup. Garnish with pomegranate arils if desired.