Grab a 9x13 inch baking dish and line it with parchment paper for easy removal later. Melt your butter over low heat, then mix it with graham cracker crumbs and granulated sugar until it's totally combined. Press this mixture firmly into the bottom of your prepared dish—I use the bottom of a measuring cup to get it really flat and compact.
In a medium bowl, beat your softened cream cheese with powdered sugar and lemon zest until it's smooth and fluffy. Spread this mixture evenly over your crust layer, then pop the whole thing in the fridge while you work on the pudding layer. This prevents the jam from soaking into the base and making everything mushy.
Whisk together the cold milk, sweetened condensed milk, vanilla instant pudding mix, and vanilla extract in a large bowl for about two minutes. You want it to thicken up nicely—it should look like soft serve ice cream consistency, not runny. Fold in your whipped topping gently until there are no white streaks remaining throughout.
Spread half of your pudding mixture over the cream cheese layer, making sure it covers everything evenly. Drop spoonfuls of strawberry jam across the pudding, then use a knife to swirl it in without going all the way to the bottom. You're creating those pretty red veins throughout, not fully mixing it together.
Repeat with blueberry jam on one side and raspberry jam on the other side of the pudding layer. This gives you those iconic red, white, and blue stripes when you slice it later—people absolutely lose their minds over how pretty it looks.
Spread your remaining pudding mixture on top as your final layer, smoothing it out completely. Cover it with plastic wrap and refrigerate for at least four hours or overnight if you can wait that long. I've made this the day before for parties and it actually tastes even better the next day.