Preheat oven to 350 degrees. Generously coat the bottom and sides of a 13" x 9" pan with non-stick cooking spray.
In a medium bowl, use an electric hand mixer to blend together softened butter, 2 cups flour and ½ cup white sugar. Mix for about 3 minutes until the mixture resembles coarse crumbs. Press into the bottom of the prepared pan pan. Bake for 17 to 20 minutes or until lightly golden at the edges. If using a metal pan, baking time will be near the lower end of the range. Remove from oven and allow to cool while preparing crust.
Meanwhile, use a hand or stand mixer to cream together the cream cheese, sour cream, and sugar. Add the eggs, milk, vanilla, lemon juice, and lemon zest. Mix just until combined and creamy. Use a wooden spoon or rubber spatula to fold in the flour and then the strawberries.
Pour cheesecake filling over warm crust and smooth out evenly. Return to oven for an additional 30 to 35 minutes until just getting lightly golden brown around the edges and the center doesn't jiggle when you shake the pan.
Remove from oven and allow to cool for an hour then cover and refrigerate for at least 3 hours or overnight before serving.