In a large mixing bowl, beat the softened cream cheese until smooth and creamy, about 2-3 minutes. Gradually add the fresh lemon juice and lemon zest, mixing until fully combined and fluffy.

In a separate chilled bowl, whip the heavy whipping cream on high speed until it begins to thicken, approximately 2 minutes. Gradually mix in the powdered sugar and vanilla extract, continuing to whip until stiff peaks form, about 1-2 more minutes.

Gently fold the whipped cream into the lemon cream cheese mixture using a spatula for a smooth, creamy filling without deflating the whipped cream, taking about 1-2 minutes.

In a 9x13 inch dish, layer half the graham crackers at the bottom. Spread half of the lemon cream cheese filling evenly over the crackers and repeat the layers, finishing with an extra layer of the lemon cream filling on top.

Cover the cake with plastic wrap and refrigerate for at least 6 hours or overnight. Garnish with lemon zest or fresh lemon slices before serving.