In a medium bowl, mix together the cracker crumbs, butter alternative, and sugar until combined.
Press the mixture into the bottom and up the sides of a 10-inch spring-form pan or into 2 regular (9-inch) pie pans.
Filling
In a medium saucepan, whisk together the coconut milk, lime juice, and sugar. Place the pan over medium heat, and bring the mixture to a simmer.
Remove the pan from the heat, add the white chocolate and stir until smooth. Allow to cool.
In a medium bowl, beat the ice cream and lime zest together with a hand mixer. Slowly beat in the cooled white chocolate mixture.
Spoon the filling into your spring form pan or divide it between the 2 pie pans, and smooth it out.
Cover the pie and freeze overnight.
Remove the pie from the freezer. If using a springform pan, run a sharp knife around inside of spring form pan to help loosen the pie. Release spring form ring from the bottom of the pan and transfer the pie to a serving plate.
Cut the pie into wedges with a knife that has been dipped into hot water and serve immediately. Store leftovers in the freezer for up to 2 months.
Notes
Tip: Instead of discarding the lime and sugar water, you can save it and use it for cocktails, or a nice lime ice tea.
Candied Lime Peel Garnish Option: Remove the peels from 4 limes, and slice the peels into strips. Bring a medium saucepan of water to a boil over medium heat. Add the peels and blanch them for a few minutes. Remove the peels and discard the water. Return the peels to the pan and cover with 2 cups sugar and 2 cups water. Simmer, covered, over low heat for 1 hour. Remove the peels and drain until almost dry. Roll in sugar and let cool.