1. Puree strawberries, sugar, and lemon juice: Blend on medium speed until smooth. Refrigerate until serving time.
2. 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.
3. 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.
4. 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.
5. Pour strawberry puree onto plate; put spider in center.