In a chilled bowl, beat the cold heavy whipping cream until stiff peaks form. Do not overmix into butter. Set aside in the refrigerator. This gives the cake its light, airy structure.
In a separate large bowl, beat the room-temperature cream cheese until completely smooth and creamy, about 2 minutes. This ensures no lumps remain in your filling.
Add the sifted powdered sugar, vanilla extract, and lemon zest to the cream cheese. Beat until combined. Gently fold in the whipped cream in three batches using a rubber spatula until uniform.
Spread a very thin layer (about 1/4 cup) of the cream mixture on the bottom of a 9x13 inch baking dish. Arrange a single layer of graham crackers over the cream, breaking pieces to fit gaps.
Spread one-third of the remaining cream cheese mixture evenly over the graham crackers. Top with an even layer of sliced strawberries.
Repeat the layers twice more. Cover the dish tightly with plastic wrap and refrigerate for at least 8 hours so the crackers soften into a cake-like texture.
