Prepare the crust. Line an 8×8-inch baking pan with parchment paper, leaving overhang on two sides for easy removal. In a medium bowl, stir graham cracker crumbs, ⅓ cup sugar, and melted butter until the mixture looks like wet sand. Press firmly and evenly into the bottom of the pan. Chill in the refrigerator while you make the filling.
Whip the cream. Pour cold heavy cream into a large bowl. Beat with a hand mixer or stand mixer on medium-high speed until soft peaks form, about 2–3 minutes. Set aside.
Make the cheesecake filling. In another large bowl, beat the softened cream cheese until completely smooth and free of lumps, about 1 minute. Add powdered sugar and vanilla. Beat again until light and creamy. Gently fold the whipped cream into the cream cheese mixture with a spatula until no white streaks remain. The filling should look thick, fluffy, and spreadable.
Assemble the bars. Spread the filling evenly over the chilled crust. Smooth the top with an offset spatula or the back of a spoon.
Prepare the strawberry topping. In a small bowl, toss diced strawberries with 2 tablespoons sugar and lemon juice. Let sit 5–10 minutes until the fruit releases a little juice. Spoon the strawberries and their juices evenly over the filling.
Chill until firm. Cover the pan loosely with plastic wrap and refrigerate at least 4 hours, preferably overnight. The bars are ready when the filling feels set and a knife inserted in the center comes out clean.
Slice and serve. Use the parchment overhang to lift the bars out of the pan. Cut into 16 squares with a sharp knife, wiping the blade between cuts for clean edges.