Make the orange, lime and raspberry sherbet recipes separately and freeze until ready to assemble. If you have an ice cream maker with a freezer insert, plan to complete this over 3 days (you’ll need to re-freeze the base overnight after each sherbet flavor). Other types of ice cream makers can handle churning the three flavors back to back.
If you’ve made your sherbet in advance, allow it to sit out at room temperature for about 15 minutes to make it easy to scoop. (If it’s freshly churned, skip this step.)
Fill a loaf pan with alternating scoops of each color of sherbet, starting with a layer in the bottom of about 6 dollops (see the photos above). Then add another layer on top, and another until the container is filled. Resist the urge to stir. Smooth out the top with a spoon.
Place in the freezer and freeze for at least 1 hour to allow it to harden to a scoopable texture (or 2 hours if working with freshly churned sherbet). Store frozen for up to 1 week: allow it to stand at room temperature for at least 10 minutes before serving to make it easy to scoop.