In a glass bowl, combine the raspberries, 2 tablespoons sugar and 1 tablespoon lemon juice and stir well. Do the same in a separate bowl with the blueberries, 1/4 cup sugar, and 1 tablespoon lemon juice. Gently press the berries with a masher to release some juices. Cover tightly with plastic wrap and let it sit in the refrigerator for about 2 hours (or overnight).
In the bowl of an electric mixer with a wire whisk, beat the heavy cream, cream cheese, and confectioners sugar until it turns to stiff peaks. Transfer to an airtight container and chill until ready to assemble.
Preheat oven to 350°F with a rack placed in the center of the oven.
Make the crisp layer. Combine flour, sugar, and butter and using a pastry blender, two forks or a food processor until it looks like coarse crumbs. Add oats and cinnamon and mix a little more. Spread in a pie pan and bake about 10 minutes or until just brown and crumbly.
Assemble the parfaits. When the berries have softened and released their juices, place about 3 tablespoons of raspberries and some juice in the bottom of 6 6-oz serving cups. Add 1/4 cup of the whipped cream mixture to each and smooth the tops. Place about 2 tablespoons of crisp on top. Add about 3 tablespoons of blueberries on top. Repeat with another whipped cream layer. If making ahead, cover each parfait glass with plastic wrap and chill in the refrigerator. This can be done up to one day ahead.
Before serving, garnish with fresh berries. Serve with additional crisp on the side, if desired.