Boil the lime juice over high heat until it's half the original volume. Let it cool down completely before continuing.
Blend the cream cheese, condensed milk and lime juice until homogeneous. You can also use a stick blender.
Whip the cream until you get soft peaks: it should be whipped but not too stiff.
Add about 1/3 of the mix to the condensed milk and mix using a spatula and folding motions. Add the rest and also fold them together.
Chop up the crackers and fold them into the mix.
Freeze the ice cream for 8 hours or overnight. Remove it from the freezer a few minutes before serving.