Preheat the oven to 350 degrees F (180 degrees C). Let cookie dough stand at room temperature for 10 to 15 minutes before baking.

Line a rimmed baking sheet with parchment paper. Press cookie dough lightly onto the parchment paper and place a second piece of parchment on top. Using a rolling pin or your hands, press dough into a thin layer all the way to the edges of the pan.

Bake in the preheated oven until just beginning to brown around the edges, 11 to 13 minutes. Let cool completely, about 20 minutes.

Meanwhile, for cream cheese frosting, beat cream cheese and butter together in a bowl with an electric mixer until smooth. Add vanilla, lemon zest, lemon juice, and salt. Gradually add confectioners' sugar until well blended. Add ⅔ of the whipped topping into the mixture and blend until just combined.

Spread ¾ of cream cheese frosting over cooled cookie crust, leaving a ¼-inch border around the edges.

Fold remaining whipped topping into remaining frosting; add mixture to a large resealable plastic bag or piping bag. Set aside.

Arrange blueberries in a single layer in a rectangular shape in the left corner of the pan. Place 5 rows of strawberries over the frosting, leaving white space in between each row. Add raspberry halves in between every 1 to 2 strawberries.

Snip the corner of the plastic bag and pipe cream cheese frosting in between each row of berries.

Serve immediately or refrigerate until ready to serve. Can be made up to 1 day ahead.