Preheat oven to 350°F (175°C). Wrap the bottom and sides of a 9-inch springform pan tightly with heavy-duty aluminum foil to prevent water from seeping in during the water bath. Ensure no gaps for water to enter.

In a medium bowl, combine graham cracker crumbs and ¼ cup granulated sugar. Pour in the melted butter and mix until thoroughly combined and moist.

Press the crumb mixture firmly into the bottom of the prepared springform pan. Use the bottom of a glass or your hands to create an even, compact layer.

Bake for 10 minutes. Remove from oven and let cool slightly while preparing the filling. Reduce oven temperature to 325°F (160°C).

In a small saucepan, combine the hulled and quartered strawberries, ¼ cup granulated sugar, and lemon juice. Cook over medium heat, stirring occasionally, until strawberries soften and release their juices, about 5-7 minutes.

Lightly mash the strawberries with a fork or potato masher. Bring the mixture to a gentle simmer.

Stir in the cornstarch slurry (1 tsp cornstarch mixed with 1 tbsp cold water) and cook, stirring constantly, for 1-2 minutes until the sauce thickens to a syrup-like consistency.

Remove from heat and let cool completely. For a smoother swirl, strain the sauce through a fine-mesh sieve, pressing on solids to extract all liquid, then discard the solids. Set aside.

In a large mixing bowl, using an electric mixer on medium speed, beat the softened cream cheese until smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl as needed.

Gradually add 1 ½ cups granulated sugar, beating until well combined and fluffy, about 2 minutes.

Beat in the all-purpose flour until just combined, about 30 seconds.

Add vanilla extract and lemon zest, mixing until thoroughly incorporated.

Add eggs one at a time, beating on low speed after each addition until just incorporated. Do not overmix after adding eggs, as this can introduce too much air and cause cracks during baking.

Gently fold in the sour cream with a rubber spatula until just combined. Be careful not to overmix.

Pour the cheesecake filling over the cooled graham cracker crust in the springform pan.

Spoon dollops of the cooled strawberry swirl over the cheesecake filling. Use a knife or skewer to gently swirl the strawberry sauce into the cheesecake mixture, creating a marbled effect. Avoid over-swirling to keep the distinct colors.

Place the foil-wrapped springform pan into a larger roasting pan. Carefully pour hot water into the roasting pan until it comes about halfway up the sides of the springform pan. This water bath helps the cheesecake bake evenly and prevents cracking.

Carefully transfer the roasting pan with the cheesecake to the preheated oven (325°F / 160°C).

Bake for 60-70 minutes, or until the edges are set but the center still jiggles slightly when gently shaken. The internal temperature should be around 150°F (65°C).

Turn off the oven, crack the door open slightly, and let the cheesecake cool in the water bath in the oven for 1 hour. This slow cooling also helps prevent cracks.

Remove the cheesecake from the water bath and the roasting pan. Carefully remove the aluminum foil. Let cool completely on a wire rack at room temperature for another 1-2 hours.

Once completely cooled, cover the cheesecake loosely with plastic wrap and refrigerate for at least 6-8 hours, or preferably overnight, to allow it to set fully.

To serve, carefully run a thin knife around the edge of the pan before releasing the springform. Slice with a hot, dry knife for clean cuts.