Combine the boiling water, sugar, and peppermint flavoring in a large container and stir until the sugar is dissolved. Let the sugar mixture stand for 5 minutes. Add the strawberries, stirring well. Using a big spoon, press the strawberry mixture through a large strainer into a pitcher or punch bowl until nothing is left in the strainer except for the strawberry pulp. Discard the pulp. Stir in the cold water and lemonade. Mix until well blended.