To prepare the strawberry compote: To a saucepan combine strawberries, sugar, lemon juice, and salt. Bring it to a boil and simmer for 10 minutes until the strawberries turn soft and mushy. Keep it aside.
To prepare the graham cracker swirl: To a medium bowl combine graham cracker crumbs, unsalted butter, and sugar. Mix it to form a sandy mixture. Keep it aside.
To prepare cheesecake base: To a large bowl, beat the cream cheese and condensed milk on a low-medium speed using a hand mixer for 3-4 minutes until well combined.
In another bowl beat the heavy cream and vanilla for 7-8 minutes until soft peaks are formed. Add the whipped cream in batches to the cream cheese mixture and fold them with a spatula gently until all the whipped cream is fully incorporated. Add in the lemon zest and fold it.
Stir in the prepared strawberry compote (reserve ¼ cup for later use) to the ice cream base and fold it 2-3 times without overmixing. Keep it aside.
Sprinkle about 2 tablespoons of the prepared graham cracker mixture to the base of the 9X5 loaf pan. Transfer about ⅓ portion of the ice cream base layer and then sprinkle some graham cracker mixture layer and repeat the same for two times until the loaf pan is full.
Stir in the reserved strawberry compote and make a swirl pattern. Cover the cheesecake ice cream with plastic wrap and refrigerate for 6 hours or overnight.
Scope and serve the strawberry cheesecake ice cream to enjoy. Store the remaining ice cream in the airtight container.