Into a large saucepan, put the unthawed raspberries and sugar. Cook over medium heat, stirring occasionally for 20-25 minutes.

Meanwhile, squeeze the juice from the lemons. Pour the juice through a fine mesh strainer into a large container. Discard the pulp.

After the sugar has dissolved and most of the raspberries burst, use a potato masher to squash the raspberries and syrup thoroughly.

Pour the mixture through the same mesh strainer you used for the lemons. Gently press the mixture until all you have left in the strainer is the pulp. Discard the pulp.

Into the same saucepan, add the water and bring to a boil. Once boiling add the water to the raspberry-lemon mixture.

Let the cordial cool, then chill in the refrigerator.

When the cordial is chilled, serve in glasses with an extra slice of lemon.