Preheat your oven to 325°F (163°C). Grease the sides of a 9-inch springform pan.
In a mixing bowl, combine graham cracker crumbs, melted butter, and sugar. Mix until the crumbs are evenly coated.
Press the mixture firmly into the bottom of the prepared springform pan to form the crust. Bake in preheated oven for 10 minutes, then remove and let cool.
In another mixing bowl, beat the softened cream cheese and sugar with an electric mixer until smooth and creamy. Gradually add the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract, sour cream, and lemon juice until fully combined.
Pour the cheesecake filling over the cooled crust and smooth the top with a spatula. Bake for 50-60 minutes, or until the center is set and slightly jiggly. Turn off the oven but leave the cheesecake inside for another hour to cool slowly.
While the cheesecake cools, prepare the cranberry topping. In a saucepan, combine cranberries, sugar, water, and lemon juice. Cook over medium heat until the cranberries burst and the mixture thickens, about 10-15 minutes.
In a small bowl, mix the cornstarch with 2 tablespoons of water to create a slurry. Add to the cranberry mixture and cook for an additional 2-3 minutes until thickened.
Allow the cranberry topping to cool before spreading it over the cooled cheesecake. Cover and refrigerate for at least 4 hours, or preferably overnight, before serving.