In a saucepan over medium heat, combine strawberries, sugar and lemon juice. Bring to a boil for about 8 to 10 minutes, stirring occasionally.
Dissolve cornstarch in a tablespoon of water and stir until smooth. Add to saucepan, whisking well to prevent lumps. Continue to cook for another 2 to 3 minutes or until sauce is thickened. Remove from heat and allow to completely cool.
In a bowl and using mixer at medium speed, beat cream cheese until fluffy. Add condensed milk and vanilla extract, and beat until smooth.
Add heavy cream and continue to beat mixture for about 3 to 5 minutes or until stiff peaks form.
Spoon half of the mixture into a 9 x 5 loaf pan. Drop dollops of the strawberry sauce onto the mixture. Sprinkle with crushed graham crackers. Spoon the remaining half of cream mixture. Drop dollops of the remaining strawberry sauce. Using a knife, swirl through the mixture. Sprinkle with more crushed graham crackers.
Cover the pan with plastic film, lightly pressing film on the surface of cream mixture (this is to prevent ice crystals from forming). Freeze for at least 6 hours or overnight. Serve frozen.