In a small bowl, mix the corn starch and about 3 T milk. Stir until corn starch has completely dissolved. Set aside.
In a saucepan, combine milk, sugar, lemon zest and pinch of salt. Stir over medium-high heat until it reaches a slow boil; stirring frequently. Reduce heat to low simmer. Whisk in the cornstarch mixture let simmer for 3 to 4 minutes, stirring constantly, until thickened. Remove from heat and set aside to cool for at least 15 minutes at room temperature.
In a medium bowl, beat the cream cheese until creamy. Add lemon juice a few tablespoons at a team, beating well after each addition.
After the milk mixture has cooled, add it to the cream cheese mixture. Stir until combined. Refrigerate for at least 4 hours.
Freeze the ice cream in your ice cream machine according to the manufacturer's instructions. Once frozen, remove from ice cream machine and add the crumbled graham crackers; stir until the graham crackers have been distributed throughout the ice cream. Serve.
Store no more than 1 day in an air-tight container.