Preheat the oven to 350 degrees F. Pulse the graham crackers and sugar in a food processor until finely ground. Add the melted butter and pulse until the mixture looks like wet sand. Press into the bottom and up the sides of a 9-inch fluted tart pan. Place on a baking sheet and bake until lightly browned and set, 12 to 14 minutes. Let cool completely on the baking sheet.
Meanwhile, make the filling: Bring the strawberries, raspberries, sugar and water to a boil in a small saucepan over medium-high heat. Reduce the heat and simmer until the liquid is syrupy and the fruit is very soft, 4 to 5 minutes. Strain through a fine-mesh sieve, pressing gently on the solids with a rubber spatula; discard the solids. Let the syrup cool.
If the cream cheese is a little stiff, soften it in the microwave in 10-second intervals. Beat the cream cheese in a large bowl with a mixer on medium-high speed until smooth and creamy, about 30 seconds. Add the condensed milk and beat until smooth. Add the berry syrup and the lemon zest and juice and beat until smooth.
In a separate large bowl, beat the heavy cream with clean beaters until medium peaks form. Gently fold the whipped cream into the cream cheese mixture using a rubber spatula until no streaks remain. Spoon the filling into the crust and spread with the back of a spoon. Cover with plastic wrap and freeze until firm, at least 4 hours.
About 10 minutes before serving, remove the pie from the freezer to soften slightly. Make the topping: Microwave the jelly in a medium microwave-safe bowl until runny, 20 to 30 seconds, then whisk until smooth. Add the strawberries and gently stir to coat. Let macerate 10 to 15 minutes. Remove the tart from the pan and transfer to a plate. Top with the strawberry mixture.
Remove the pie from the freezer and let it sit for about 10 minutes before slicing.