Set the oven rack to the middle position and preheat oven to 350°F. Spray a half-size (18x13x1-inch) rimmed baking sheet with nonstick baking spray. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter on medium speed until smooth. Gradually add the sugar and continue beating until light in color and fluffy, about 3 minutes.
1¼ cups unsalted butter, 2½ cups granulated sugar
Beat in eggs, one-at-a-time, until well combined.
5 large eggs
Beat in the lemon juice and vanilla.
1 tablespoon fresh lemon juice, 1½ teaspoons pure vanilla extract
In a separate large bowl, whisk together the flour, gelatin powder, baking soda and salt.
3 cups all-purpose flour, 3 ounces strawberry-flavored gelatin, 1 teaspoon baking soda, 2 teaspoons kosher salt
Turn mixer to low speed. Starting with the flour mixture, beat in the flour and buttermilk alternately to the butter mixture in 5 additions (beginning and ending with flour) beating just long enough after each addition to be blended.
1¼ cups buttermilk
Gently fold in the strawberries.
1 cup diced fresh strawberries
Spread batter into the prepared baking sheet.
Bake for 30-40 minutes, or until a toothpick inserted in the middle comes out clean.
Cool the cake on a cooling rack before frosting.
While the cake cools, make the frosting. In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese, butter, and salt on medium speed until creamy and lighter in color, about 2 minutes.
16 ounces cream cheese, ½ cup unsalted butter, ½ teaspoon kosher salt
Beat in the fresh lemon juice, lemon zest, and mashed fresh strawberries just until blended.
2 lemons, ¾ cup diced fresh strawberries
Turn the mixer to low speed and slowly add enough powdered sugar until the desired consistency is achieved. If the mixture is too thick, add more lemon juice or mashed strawberries.
3½ cups powdered sugar
Frost the cooled cake with the strawberry cream cheese frosting, slice, and serve.