In a large mixing bowl, use a hand mixer to beat the softened cream cheese until it achieves a light and fluffy texture, approximately 2 minutes.
Add the instant lemon pudding powder, vanilla extract, and lemon juice to the cream cheese. Blend the mixture with a hand mixer until it is uniform in consistency and achieves a bright yellow color.
Gradually add the milk to the mixture, continuously mixing to ensure that minimal lumps remain.
Gently fold in the Cool Whip into the mixture using a rubber spatula, ensuring it is fully integrated without losing its airiness.
In a 9×13-inch casserole dish, spread 1/2 cup of the pudding mixture across the bottom of the dish. Arrange a single layer of graham crackers over the mixture, breaking pieces as necessary to fit the shape of the dish and cover any gaps.
Pour one-third of the remaining pudding mixture over the graham crackers, spreading it evenly across the layer.
Repeat the layering process with graham crackers and the pudding mixture, ensuring even distribution.
Place the assembled cake in the freezer for 4 hours or refrigerate it overnight to set.
Prior to serving, remove the cake from the freezer and allow it to sit at room temperature for 15-20 minutes to soften. Garnish with lemon zest, fresh raspberries, or other optional toppings as desired.