Bake the pie crust in a 9″ pie plate per package directions. Let cool.
Lower oven temperature to 350°F. Beat egg yolks, milk, lime juice and zest in a medium bowl until creamy. Pour lime custard evenly in pie crust and bake 15 minutes until just set. Let cool and refrigerate until thoroughly chilled, at least one hour.
Raise oven temperature to 425°F. Add sugar and water in a medium saucepan and bring to a boil. Continue boiling until the temperature reaches 234°F (about 8 minutes). In a stand mixer with a whisk attachment or using an electric mixer, beat the egg whites and cream of tartar until soft peaks form. While mixing, pour the hot syrup over the egg whites very carefully and continue to beat until the whites are stiff and glossy. Spread meringue over the pie filling and bake for 5-7 minutes until the tips are golden brown.
Refrigerate any leftovers covered with plastic wrap or aluminum foil.
Double the filling for a deep dish pie pan and increase the bake time to 20-25 minutes.
Keep a close eye on the meringue topping while it is in the oven so it does not overcook.