Bring the raspberries, syrup, and lemon juice to a simmer in a heavy medium saucepan over low heat. Simmer, stirring occasionally, until the berries are very soft, about 8 minutes.
Sprinkle the cornstarch over 2 teaspoons cold water and stir to dissolve. Pour into the simmering raspberry mixture. Cook, stirring occasionally, until the sauce thickens, about 5 minutes.
Strain through a fine-mesh sieve into a bowl; discard the seeds. Cool completely, then cover and refrigerate until ready to use.