Three-Berry Syrup

In a small heavy saucepan simmer cranberries and raspberries including their syrup, covered, until cranberries have burst, about 10 minutes. Force mixture through a fine sieve into a bowl, pressing hard on solids, and return liquid to pan. Stir in sugar, water, strawberry syrup, and lemon juice and simmer, uncovered, until sugar is dissolved and mixture has thickened slightly, 5 to 10 minutes. Stir in strawberries and simmer until heated through, about 2 minutes.

Serve syrup warm or at room temperature. The syrup keeps, covered and chilled, 1 week .