In a saucepan, combine the berries, water, sugar, and lemon juice. Bring the mixture to a simmer over medium heat, stirring occasionally.
Once the mixture starts to simmer, reduce the heat to low and let it simmer for about 10-15 minutes, or until the berries have softened, and the liquid has thickened slightly.
Remove the saucepan from heat and let the mixture cool for a few minutes. Strain the syrup through a fine mesh sieve into a bowl, pressing the berries with the back of a spoon to extract as much liquid as possible. Discard the solids.
Allow the syrup to cool completely before transferring it to a clean, airtight bottle or jar. Store the syrup in the refrigerator.