In a medium saucepan, combine the pomegranate juice, sugar, lemon juice, and water. Bring to a simmer over medium heat, stirring until the sugar is dissolved.

Remove from heat and let cool for 10 minutes. Stir in the rosewater.

Pour the mixture into a shallow dish and freeze for 1 hour.

Remove from the freezer and use a fork to break up any ice crystals. Return to the freezer and repeat this process every 30 minutes for 3 hours, or until the sorbet is firm and slushy.

Once the sorbet is firm, transfer to an airtight container and freeze for at least 1 hour before serving.

Serve the sorbet in chilled bowls or glasses and garnish with fresh pomegranate seeds, if desired.