Pulse your graham crackers in a food processor until you get fine crumbs—not powder, but not chunky either. Pour them into a small bowl with the melted butter and 1/4 cup granulated sugar. Mix until it looks like wet sand, then press it firmly into the bottom of a 9-inch springform pan. Chill for 15 minutes while you prep everything else.
Grab a large mixing bowl and add your softened cream cheese. Beat it on medium speed for about 2 minutes until it's completely smooth and creamy. Add the powdered sugar, lemon juice, lemon zest, and salt. Beat again for another minute until everything's fully combined and there are zero lumps visible.
In a separate bowl, pour your heavy whipping cream and whip it with an electric mixer on medium-high speed. You're looking for stiff peaks—basically when you lift the beaters, the peaks should stand straight up without flopping over. This takes about 3-4 minutes depending on your mixer.
Gently fold the whipped cream into your lemon-cream cheese mixture using a spatula. Do this slowly and carefully because you want to keep all those air bubbles from deflating. I fold about a third of the whipped cream in first, then fold in the rest—trust me on this, it's easier to combine when you do it in stages.
Pour the entire lemon filling over your chilled crust and smooth the top with a spatula. You want it nice and even, but don't stress about perfection—this isn't a competition. Refrigerate for at least 4 hours or until it's completely set and firm to the touch.
While you're waiting, prep your strawberries by slicing them and tossing them gently with the chopped fresh mint. Store them in a separate container in the fridge so they stay fresh and don't release all their liquid onto the cake prematurely.
When you're ready to serve, run a thin knife around the edges of the springform pan and carefully release the sides. Top with your minty strawberries right before serving, or arrange them on individual slices if you prefer. This no bake lemon icebox cake stays fresh in the fridge for up to 4 days.