Combine in a blender:

Puree, then strain through a fine-mesh sieve into a medium bowl, pressing firmly to extract as much juice as possible; discard the seeds. Stir in:

Refrigerate the sorbet base until cold, overnight if possible, or quick-chill in an ice water bath.

Taste and add more sugar or lemon juice if needed, stirring until the sugar is completely dissolved, 2 to 3 minutes. Pour the base into an ice cream maker and freeze as directed. Serve immediately or transfer to a container with a tight-fitting lid and freeze.