In a saucepan, combine the blueberries, sugar, water, and lemon juice.
Place the saucepan over medium heat and bring the mixture to a simmer. Stir occasionally to dissolve the sugar and prevent sticking.
If you prefer a thicker syrup, you can mix the cornstarch with a small amount of water to create a slurry. Add the slurry to the blueberry mixture and stir well.
Continue simmering the mixture for about 10-15 minutes, or until the blueberries have softened and released their juices. If you added the cornstarch, the syrup will thicken slightly.
Remove the saucepan from the heat and let the syrup cool for a few minutes.
If you prefer a smooth syrup, you can use an immersion blender or a regular blender to puree the mixture until smooth. Alternatively, you can leave it chunky for a textured syrup.
Strain the syrup through a fine-mesh sieve to remove any remaining solids. Press the mixture against the sieve with the back of a spoon to extract all the liquid.
Allow the syrup to cool completely before serving. It will thicken slightly as it cools.
Serve over pancakes, waffles, French toast, oatmeal, or other dishes as desired.