Add strawberries, sugar and lime juice to a medium sized pot and bring to boil over medium high heat.
Continue to boil for additional 5-7 minutes until juices have released, berries have softened and sauce has thickened a little.
Remove berries from heat and allow them to cool then place in refrigerator for 1 hour to completely cool them down.
For the Ice Cream
Add cream cheese to bowl of stand mixer or medium sized bowl if using hand mixer.
Beat on medium high speed then slowly add in condensed milk and vanilla extract and mix until completely smooth.
Turn off mixer and fold whipped cream into cream cheese mixture using a spatula.
Once whipped cream is folded in, carefully fold strawberries into batter only folding 3-4 times just until the strawberries have distinctly swirled through batter (don’t over fold the strawberries because you will turn the entire ice cream mixture red).
To freeze, alternate adding ice cream mixture and graham cracker crumbs to freezer safe containers. Freeze for at least 5-7 hours then serve.