Combine the raspberries, syrup, and lemon juice into a bowl. Process, in two batches, in a food processor until smooth. Strain through a fine-mesh strainer into a medium bowl; discard the seeds. Refrigerate until well chilled, at least 2 hours.
Pour the purÈe into an ice cream machine and churn according to the manufacturerís instructions. Pack into an airtight container and freeze for at least 2 hours before serving.
To serve, scoop into dessert bowls and drizzle with the raspberry coulis.