Preheat oven to 350°F (175°C). Line the bottom of a 9-inch springform pan with parchment paper.
In a medium bowl, combine graham cracker crumbs, 0.375 cups sugar, and melted butter. Press evenly into the bottom of the prepared springform pan to form the crust.
Bake the crust for 8-10 minutes, or until lightly golden. Remove from oven and let cool completely.
While the crust cools, prepare the strawberry swirl. In a small saucepan, combine sliced strawberries, 0.25 cups sugar, and lemon juice. Cook over medium heat, stirring occasionally, until strawberries have softened and the mixture has thickened, about 10-15 minutes. Mash some of the strawberries with a fork. Let cool.
In a large bowl, beat cream cheese until smooth and creamy. Gradually beat in 1.5 cups sugar until well combined.
Add eggs one at a time, beating well after each addition. Stir in vanilla extract, cocoa powder, red food coloring, and sour cream until just combined. Do not overmix.
Pour half of the red velvet cheesecake batter over the cooled crust. Dollop spoonfuls of the cooled strawberry mixture over the batter. Swirl the strawberry mixture into the batter using a knife or skewer.
Pour the remaining red velvet cheesecake batter over the swirled mixture. Dollop more strawberry mixture on top and swirl again.
Bake in a water bath (place the springform pan in a larger roasting pan and fill the larger pan with about 1 inch of hot water) for 55-65 minutes, or until the edges are set and the center is slightly jiggly.
Turn off the oven and leave the cheesecake inside with the door slightly ajar for 1 hour to prevent cracking. Remove from oven and let cool completely on a wire rack.
Cover the cheesecake and refrigerate for at least 4 hours, or preferably overnight, before serving.
Notes
For best results, ensure all ingredients for the cheesecake filling are at room temperature.