Preheat your oven to 350°F. Pulse the 6 crushed graham crackers, chopped almonds, brown sugar, salt, and melted butter together in a food processor until the mixture resembles wet sand with some texture remaining—you want it to hold together but not become a paste. Press this mixture firmly and evenly into the bottom of a 9x13 inch baking dish, using the bottom of a measuring cup to create an even layer. Bake for 10 minutes until lightly golden, then remove from the oven and let cool completely to room temperature, about 10-15 minutes.
Spread the softened vanilla ice cream (about 1.5 pints) evenly over the cooled crust in an even layer—I find an offset spatula dipped in warm water works beautifully for this. Mix the lemon zest into the blackberry jam to brighten the flavor slightly, then spread the jam mixture over the ice cream layer. Crumble the remaining 3 graham crackers by hand and sprinkle them over the jam layer, then top everything with the remaining softened ice cream (about 1.5 pints), spreading it smooth.
Freeze the ice cream cake for at least 2 hours until the ice cream is completely firm. Once frozen solid, spread the whipped topping evenly across the top of the cake using an offset spatula or the back of a spoon, creating an even layer that will hold the berries.
Arrange the raspberries and blackberries on top of the whipped topping in a flag pattern: create three horizontal stripes using raspberries for two stripes and blackberries for one stripe, alternating colors. For a classic American flag look, use two raspberry stripes on the bottom, one blackberry stripe in the middle, and finish with a raspberry stripe on top (or adjust to your preferred color pattern). Keep the cake in the freezer until ready to serve, then slice and serve immediately so the cake doesn't melt too quickly.