Lightly grease a 9x13-inch baking dish with a thin layer of butter or nonstick spray. For the prettiest presentation, use a glass dish so the layers are visible.

In a medium bowl, combine the graham cracker crumbs, melted butter, and granulated sugar. Stir until all the crumbs are evenly coated and the mixture looks like wet sand. Pour the crumb mixture into the prepared pan, then press it down firmly using the bottom of a measuring cup or flat glass, paying special attention to the corners. Chill the crust in the refrigerator for at least 15–20 minutes while you prepare the next layer.

If you prefer a super-firm crust and don’t mind turning on the oven, bake the crust at 350°F (175°C) for 8–10 minutes, then cool completely before proceeding. This step is optional and will make the dessert no longer fully no-bake.

In a large mixing bowl, beat the softened cream cheese with an electric mixer on medium speed until smooth and fluffy, 1–2 minutes. Add the powdered sugar and vanilla extract and beat again until fully combined and creamy, scraping the sides of the bowl as needed. Gently fold in 1 cup of whipped topping with a spatula until just combined and light. Spread the cream cheese mixture evenly over the chilled crust, smoothing it all the way to the edges without disturbing the crust. Return the pan to the refrigerator while you make the pudding layer.

In another large bowl, whisk together the instant lemon pudding mix and 2 1/2 cups of cold milk. Whisk for 2–3 minutes until the mixture thickens and is smooth and pourable but holds soft peaks. If the pudding seems too thick, whisk in up to an additional 1/2 cup milk, a little at a time. Stir in the fresh lemon juice and lemon zest, if using, for a brighter lemon flavor.

Remove the pan from the refrigerator and gently spoon the lemon pudding over the cream cheese layer. Use an offset spatula or the back of a spoon to spread it evenly to the edges, working slowly to avoid disturbing the layer underneath. Place the pan back in the refrigerator for at least 10–15 minutes to allow the pudding to set a bit more.

Once the pudding layer has thickened slightly, spread the remaining 2 cups of whipped topping evenly over the top. Smooth it for a clean finish or use a spatula to create gentle swirls, as you prefer.

Cover the pan loosely with plastic wrap or foil, taking care not to press down on the whipped topping. Chill in the refrigerator for at least 4 hours, or overnight for best flavor and the cleanest slices.

Just before serving, garnish the top with lemon zest, thin lemon slices, and/or crushed graham crackers or white chocolate shavings, if desired. Use a sharp knife to cut into squares, wiping the knife between cuts for neat layers, and lift pieces out with a small spatula.