Make crust: Combine graham crackers and sugar in a food processor. Process until finely ground. Add butter; pulse to combine. Transfer to a 9-inch pie plate. Press evenly over bottom and sides. Freeze until firm, about 30 minutes.
Make filling: Wipe out processor's bowl and add 2 cups raspberries, lemon juice and sugar. Process into a thick puree. Strain through a fine sieve into a medium bowl. Discard solids.
In a separate medium bowl, beat together cream and yogurt with an electric mixer on high speed until stiff peaks form. Stir in berry mixture. Pour into crust and top with remaining berries. Freeze until very firm, at least 6 hours. Let stand for about 15 minutes at room temperature before slicing and serving.