Boil blueberries and sugar in a small saucepan till berries burst and the mixture has thickened. (7-8 minutes) Cool completely and chill.
Cheesecake Ice Cream Base
Beat cream cheese and sugar till smooth. Beat in the cream, milk, vanilla, lemon juice, and zest. Chill for several hours or till cold. Churn ice cream in an ice cream maker.
To freeze:
Set aside 1/2 cup of the blueberry sauce.
In a freezer safe container, add spoonfuls of the ice cream base, sauce, and graham cracker pieces in multiple layers. Swirl gently if desired.
Cover and freeze for 2-3 hours or till hardened. Serve with reserved blueberry sauce if desired.