Combine strawberries, blueberries, lemon zest, lemon juice and sugar in a medium saucepan over medium heat.
Bring to a boil, stirring to help sugar dissolve, then reduce to a gentle simmer. Cook for about 10 minutes, or until berries have broken down and mixture is thick and syrupy. Carefully transfer to a blender and blend until smooth. Pass through a fine mesh sieve into a bowl, using a rubber spatula to press fruit puree through, then discard pulp. Refrigerate until ready to use.
Preheat oven to 375° F. Line a 9×5-inch loaf pan with a double layer of parchment paper, allowing a few inches of overhang on each side.
Combine shortbread cookie crumbs and butter in a bowl and press firmly into the bottom of the pan and up 1 inch along the sides. Bake until crisp and lightly golden, 10-12 minutes, then cool completely. Run a knife around the edge of the crust to loosen, then use the parchment paper sling to lift up and release the crust from the pan. Carefully return it and transfer to a freezer; chill at least 30 minutes.
Scoop and drop sorbet flavors in an alternating pattern over the bottom of the loaf pan. Use a spoon or offset spatula to smash it down into the pan. Repeat layering and smooshing sorbet until the pan is full and all of the sorbet has been used; spread the surface smooth. Freeze, covered with plastic wrap, until firm, at least 4 hours.
To serve, wipe the outside of the pan with a hot, wet towel to release the sorbet, then use the parchment paper to lift the sorbet loaf out of the pan and transfer it to a platter. Slice into 1-inch thick slices and spoon berry sauce on top.