Line an 8-by-4-by-3-inch loaf pan with plastic wrap, leaving enough overhang in each direction to completely cover the top. Measure out 2/3 cup of the strawberry preserves. Set both aside.
Beat the cream cheese in the bowl of a stand mixer fitted with the paddle attachment on high until fluffy, about 4 minutes, stopping to scrape down the sides of the bowl as needed. Add the sour cream and lemon zest and beat until combined, about 30 seconds more. Transfer to a large mixing bowl.
Swap the paddle for the whisk and whip 1/2 cup of the cream along with the powdered sugar on medium-high until stiff peaks form, about 3 minutes. Fold into the cream cheese mixture and transfer to a zip-top bag.
Cover the bottom of the prepared loaf pan with a layer of graham crackers. Snip the corner of the zip-top bag and pipe in approximately 1/4 to 1/2 cup of the whipped cream mixture and smooth with a spoon or spatula. (It's totally fine to eyeball this; just know you'll end up with 6 cream layers.) Top with about 3 tablespoons of preserves (again, it's fine to eyeball), followed by 1/2 teaspoon of pepper and another layer of whipped cream.
Continue layering — crackers, whipped cream, preserves, pepper, whipped cream, crackers — until you have 4 layers of graham crackers (see Cook's Notes). Fold the excess plastic wrap over the cake and refrigerate 8 hours and up to 24.
When ready to serve, whip the remaining 1 cup cream in the bowl of a stand mixer on medium-high until stiff peaks have almost formed. Drop the mixer to low and work in the remaining 1/3 cup strawberry preserves and 1 teaspoon black pepper. Boost the speed back to medium-high until stiff peaks form.
Pull back the plastic wrap and invert the cake onto a serving dish. Remove the plastic wrap completely and frost with the strawberry whipped cream. Slice and serve immediately.