Preheat a small saucepan over medium heat and combine the blueberries, sugar, and lemon juice. Stir occasionally while the berries soften and release their juices.

In a small bowl, whisk together the cornstarch and water until smooth. Pour it into the blueberry mixture and continue cooking for 2–3 minutes until the sauce thickens slightly. Remove from the heat and allow it to cool completely.

In a separate bowl, combine the graham cracker crumbs and melted butter until evenly coated. Set aside for later.

In a large mixing bowl, beat the softened cream cheese until smooth and creamy. Add the sweetened condensed milk, vanilla extract, and lemon juice, then mix until fully combined and silky.

In another chilled bowl, whip the heavy cream until stiff peaks form. This helps create the light and fluffy texture of the ice cream.

Gently fold the whipped cream into the cream cheese mixture using a spatula. Mix slowly and carefully so the mixture stays airy and smooth.

Spoon half of the ice cream mixture into a freezer-safe container. Add spoonfuls of the blueberry sauce and sprinkle some graham cracker crumbs over the top. Repeat with the remaining ice cream mixture, blueberry sauce, and graham cracker crumbs.

Use a butter knife or skewer to gently swirl the blueberry sauce through the ice cream to create a marbled cheesecake effect. Avoid overmixing so the swirls remain visible.

Cover the container tightly with a lid or plastic wrap and freeze for at least 6 hours or overnight until firm.

Before serving, let the ice cream sit at room temperature for about 5 minutes for easier scooping. Serve topped with extra blueberries or graham cracker crumbs if desired.