Combine strawberries, sugar, and lemon juice in a medium saucepan over medium heat. Cook for 8-10 minutes, mashing occasionally, until berries break down and mixture thickens to a loose jam consistency. Strain through a fine-mesh sieve into a bowl, pressing to extract all liquid; discard seeds. Let cool completely, about 30 minutes. You should have about 3/4 cup sauce.

In a large bowl, beat softened cream cheese with an electric mixer until completely smooth, about 2 minutes. Add sweetened condensed milk, vanilla, and salt; beat until well combined and no lumps remain.

In a separate large bowl, whip cold heavy cream with an electric mixer on medium-high speed until stiff peaks form, about 3-4 minutes. The cream should hold its shape when you lift the beaters.

Gently fold about one-third of the whipped cream into the cream cheese mixture to lighten it, then fold in the remaining cream in two additions. Use a spatula and work carefully to keep the mixture airy.

Spread one-third of the ice cream base into a 9x5-inch loaf pan. Drizzle with 3 tablespoons of strawberry sauce and sprinkle with one-third of the graham cracker chunks. Repeat layers twice more, ending with graham crackers on top. Use a knife to swirl the sauce gently through the layers - don't overmix or you'll lose the ribbon effect.

Cover tightly with plastic wrap and freeze for at least 6 hours, preferably overnight, until completely firm. Let sit at room temperature for 5 minutes before scooping for the best texture.