You'll need an ice cream maker for this recipe. Make sure to prepare it ahead of time according to the manufacturer's directions.
In a small saucepan, combine the sugar and water. Bring to a boil over low-medium heat, stirring until the sugar is completely dissolved. Remove from heat and let it cool.
1 cup granulated sugar, ½ cup water
Place the raspberries into a blender, and process until smooth.
4 cups fresh or frozen raspberries
Pour the raspberries through a fine-mesh sieve into a bowl to remove the seeds. Use a spatula to press the mixture through the sieve.
Stir in the cooled simple syrup, lemon juice, and raspberry liqueur (if using). If desired, pour the mixture through a strainer a second time.
1 tablespoon lemon juice, 1 tablespoon raspberry liqueur
Cover the bowl and refrigerate the mixture for at least 1 hour, or until completely chilled.
Pour the chilled mixture into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency.
Transfer the sorbet to an airtight container and freeze for 4-6 hours, or until firm.