Place raspberries in a wire-mesh strainer; press with back of spoon against the sides of the strainer to squeeze out 1/3 cup juice. Discard pulp and seeds remaining in strainer.
Combine raspberry juice and cornstarch in a small saucepan; cook over medium heat, stirring constantly, until thickened and bubbly. Let mixture cool slightly. Add sugar and yogurt to raspberry mixture, stirring until blended; set aside.
Place apple and pear slices in a bowl; sprinkle with lemon juice, and toss gently. Arrange apple, pear, grapes, and cheeses on 2 lettuce-lined salad plates. Serve with dressing mixture.