In a blender, combine the mixed frozen berries, sugar, and lemon juice. Blend until smooth. Strain the berry puree through a fine mesh sieve to remove seeds. Set aside.
In another bowl, mix the chocolate cookie crumbs and melted butter until well combined.
Press the mixture into the bottom of a springform pan or a lined cake pan to form the cake base. Place it in the freezer to set while you prepare the ice cream layers.
Remove the cake base from the freezer and spread the softened vanilla ice cream evenly over the base. Place the pan back in the freezer for about 30 minutes to let the vanilla layer firm up slightly.
Once the vanilla layer is set, spread the softened berry-flavored ice cream over it. Drizzle half of the berry puree over the berry ice cream layer, and use a knife or skewer to create swirls. Return the pan to the freezer for another 30 minutes.
After the berry layer has set a bit, spread the softened chocolate or fudge ripple ice cream on top. Drizzle the remaining berry puree over the chocolate layer and swirl it with a knife.
Cover the cake with plastic wrap and freeze for at least 4-6 hours, or until completely firm.
