Add the graham crackers to a food processor and pulse until finely ground. Add the butter and brown sugar and pulse until mixture resembles coarse sand.
Pour the graham cracker mixture into the bottom of a 9x13 baking sheet. Press the graham crackers into to bottom of the pan until firm. Place the crust in the refrigerator to chill while you assemble the cheesecake mixture.
In a large bowl, combine the cream cheese, powdered sugar, and vanilla. Beat until well combined.
Fold in the whipped topping.
Spread the mixture over the top of the graham cracker crust in an even layer. Place in the refrigerator to chill for at least four hours.
When ready to serve, add the chopped strawberries, blueberries, lemon juice, and sugar to a large bowl. Toss to combine, then spread the fruit mixture over the top of the cheesecake.
Cut into bars and serve.