Preheat to 350 degrees F. Lightly butter a 9 inch round springform pan.
Process crumbs, pecans and sugar until blended, then add butter and pulse to mix. Empty crumbs into pan and press tightly. Bake for about 10 minutes. Let cool completely on a wire rack.
Soften the sherbet a bit, then place it in a bowl and mash it around to soften even more. Spread evenly over cooled crust, cover with a layer of plastic wrap and freeze until firm. Repeat with the raspberry sherbet (or sorbet), softening and then spreading over the lime sherbet.
Cover with plastic wrap and freeze until firm.
Make the raspberry sauce. Puree raspberries, 2 tablespoons of the sugar and fresh lemon juice in a food processor. Taste. Add remaining sugar and lemon juice as needed, and blend again to dissolve sugar. Strain through fine wire sieve into a bowl. Cover and refrigerate until chilled.
When ready to serve, whip heavy cream, confectioners' sugar and vanilla in medium bowl with an electric mixer or in the food processor.
Before serving, loosen the cake from the pan and remove sides. With a knife dipped in warm water, cut into triangles. Garnish individual slices with whipped cream and raspberry sauce.
Alternatively, you can garnish the cake before cutting it. I like to do one slice at a time so that I can keep the ungarnished cake tightly wrapped and frozen.