In the bowl of a stand mixer with a paddle attachment (or hand mixer or just using a whisk), whisk whipped cream until stiff peaks form. Scoop out whipped cream and place into another bowl, then set aside for later.
Using the same bowl on your stand mixer and a paddle attachment (or just using a hand mixer or whisk), beat cream cheese until smooth. Add in sweetened condensed milk, vanilla extract, and lemon juice and zest, then beat in until smooth.
Fold cream cheese mixture into the whipped cream carefully, using a silicone spatula and gently scooping from the bottom to fold the mixture together, so you don't deflate the whipped cream.
Pour half of your cream mixture into a 9x5" loaf pan. Use a spoon to place spoonfuls of cherry filling onto the layer of ice cream base, then swirl the cherries into the cream with a butter knife.
Pour remaining cream mixture on top and repeat, then sprinkle graham crackers on top. Freeze for about 4-8 hours.