Easy Caribbean Pineapple-Lime Ice Cream (without an ice cream maker!)

This is super easy and very delicious!  I love the combination of the crushed pineapple with the lime juice, plus the sweetness of the heavy cream and condensed milk.  So creamy and delicious!  Enjoy!
-1 (20 oz) can crushed pineapple (keep the juice too)
-1 (14 oz) can sweetened condensed milk
-1 small lime
-2 tsp vanilla extract
-1 cup heavy cream
Combine the pineapple (and the juice) and the milk.  Mix well.  Zest the lime and add the lime to the mix.  Also, add the juice of the lime.  Mix well.  Stir in the vanilla.
Beat the heavy cream until stiff peaks form.  Fold into the pineapple mixture.
Pour mix into 9x5 inch loaf pan or 2 quart dish.  Cover and freeze for at least 3 hours.