In a medium bowl, mix the graham cracker crumbs with the melted butter until well combined. Press this mixture firmly into the bottom of a 9-inch springform pan to create the crust.
Bake the crust in the preheated oven for about 10 minutes or until lightly golden. Remove it from the oven and let it cool.
In a large mixing bowl, beat the softened cream cheese with granulated sugar using an electric mixer until smooth and creamy. Add the vanilla extract and sour cream, mixing until fully incorporated.
Add the eggs one at a time, mixing gently after each addition until just combined. Avoid overmixing.
In a separate bowl, toss the fresh cranberries with powdered sugar, lemon juice, and lemon zest until evenly coated. Fold the cranberries gently into the cheesecake batter.
Pour the cheesecake batter over the cooled crust.
Bake in the oven for 55-65 minutes or until the edges are set and the center has a slight jiggle.
Once baked, turn off the oven and let the cheesecake cool in the oven with the door slightly ajar for about 1 hour to prevent cracking.
After it has cooled, refrigerate the cheesecake for at least 4 hours, or preferably overnight, to allow it to set fully.
Before serving, you can garnish with extra cranberries or a sprinkle of powdered sugar for an elegant finish.