Using a wooden spoon, push raspberries through a handheld wire strainer to puree.
In a medium bowl, whisk together 2 tablespoons raspberry puree, lemon juice, vinegar, and sugar.
In a slow but steady stream, whisk in olive oil until emulsified. Season with salt and pepper. Vinaigrette can be made 1 day in advance and stored in an airtight container in the refrigerator.