Step 1: Combine strawberries, 1/4 cup sugar, and lemon juice in a small saucepan over medium heat. Simmer for 10-15 minutes until thickened, then chill completely.
Step 2: In a large bowl, beat the softened cream cheese and remaining 1 cup sugar until smooth and fluffy.
Step 3: Slowly whisk in the milk, vanilla, and salt until the sugar is dissolved, then stir in the heavy cream.
Step 4: Cover and refrigerate the mixture for at least 4 hours (overnight is best) to ensure it is thoroughly chilled.
Step 5: Churn the mixture in an ice cream maker according to the manufacturer's directions, usually about 20-25 minutes.
Step 6: Gently fold in the chilled strawberry sauce and crushed graham crackers, then transfer to a container and freeze for 4-6 hours until firm.