Preheat your oven to 325°F (160°C).

In a mixing bowl, combine the graham cracker crumbs, melted butter, and ¼ cup of sugar. Mix until well combined and crumbly.

Press the graham cracker mixture into the bottom of the springform pan to form an even layer. Bake for 10 minutes, then remove from the oven and let cool.

While the crust is baking, prepare the cranberry swirl. In a saucepan, combine cranberries, ½ cup of sugar, ¼ cup of water, and 1 teaspoon of lemon juice. Cook over medium heat until the cranberries burst and the mixture thickens (about 10 minutes). Set aside to cool.

In a large mixing bowl, beat the softened cream cheese with ½ cup of sugar until smooth. Add eggs one at a time, mixing well after each addition. Stir in vanilla extract and lemon juice until combined.

Pour the cream cheese mixture over the cooled crust.

Drop spoonfuls of the cranberry mixture onto the cheesecake filling, and use a toothpick or skewer to swirl it gently through the filling for a marbled effect.

Bake the cheesecake in the preheated oven for 50-60 minutes, or until the center is set and the edges are slightly puffed.

Turn off the oven and leave the cheesecake inside for another hour to cool gently.

Remove the cheesecake from the oven and let it cool to room temperature. Refrigerate for at least 4 hours or overnight for best results before serving.