Puree strawberries, sugar, and lemon juice: Blend on medium speed until smooth. Refrigerate until serving time. To make "bodies," place cookies on a waxed-paper-lined baking sheet. Put a small scoop of ice cream on top of each cookie and freeze until hard, about 30 minutes. Remove bodies from freezer and poke 3-inch pieces of licorice into sides for legs. If ice cream is very hard, poke holes with a toothpick first. Freeze for a few minutes to harden. Cover bodies with thick layer of chocolate sauce. Before sauce hardens, press 2 chocolate chips onto front of each one for eyes. Freeze again until ready to serve. Pour strawberry puree onto plate; put spider in center.
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