How to Make It
Wrap cake in plastic wrap and freeze for 30 minutes. Preheat oven to 325°F. Spread coconut in a single layer on a baking sheet and toast until lightly browned, 13 to 15 minutes, stirring occasionally. Transfer to a bowl to cool.
Let sherbet stand at room temperature for 15 minutes to soften. (Standing times may vary; sherbet should be soft enough to spread with a spatula or butter knife.) Using a serrated knife, slice cake horizontally into 4 equal layers. Place bottom cake layer on a serving plate. Using a small offset spatula, spread peach sherbet in an even layer over cake. Top with second cake layer, pressing down lightly, and spread evenly with raspberry sherbet. Top with third cake layer, pressing lightly, and spread evenly with pineapple sherbet. Top with remaining cake layer. Wrap cake in plastic wrap and freeze for at least 4 hours.
Using an electric mixer at high speed, beat cream until foamy; gradually add confectioners' sugar, lime juice and zest, if desired, beating until stiff peaks form. Spread whipped cream mixture on top and sides of cake. Gently press coconut onto sides of cake; sprinkle top evenly with coconut. Freeze for 1 hour.