In a small saucepan, combine strawberries, sugar and lemon juice. Mix together cold water and cornstarch, add to saucepan. Bring to a boil, then immediately lower the heat and simmer gently for 3-5 minutes or just until slightly thickened. Remove from heat. Mash with a fork so only small chunks remain. Set aside to cool, then chill thoroughly.
In a large mixing bowl, use an electric mixer to whip cream cheese until fluffy. Add condensed milk and continue to whip until fully combined and smooth. In a separate bowl, use mixer to whip heavy cream and vanilla together until stiff peaks form.
Fold vanilla whipped cream into cream cheese mixture by hand.
Pour half of ice cream mixture into the bottom of a 9 x 5 inch loaf pan. Dollop ½ strawberry mixture over cream and top with ½ crushed graham crackers. Use the sharp end of a knife to swirl through cream. Repeat layers with ice cream, strawberries and graham crackers. Swirl with a knife.
Freeze until set around 8 hours, or overnight.
Scoop into dishes or waffle cones for serving.