Place the blueberries, granulated sugar, water, and lemon juice in a 2-quart (1.9-liter) saucepan. Stir until the sugar is evenly moistened.

Set the saucepan over medium heat: Cook for 4 to 6 minutes, stirring occasionally, until the sugar dissolves and the liquid begins bubbling gently around the edges.

Reduce the heat to medium-low and simmer for 8 to 10 minutes. Stir occasionally and lightly crush the berries with a potato masher or the back of a spoon. The berries should burst, and the liquid should become deep purple and slightly syrupy.

Remove the pan from the heat when the syrup lightly coats the spoon but still pours easily. It will thicken further as it cools. If the mixture becomes thick like jam, stir in 1 to 2 tablespoons of water before straining.

Place a fine-mesh sieve over a heatproof bowl or measuring cup. Carefully pour in the blueberry mixture. Allow the liquid to drain, then press the berries gently with the back of a spoon. Avoid forcing large amounts of pulp through the sieve, which can make the syrup cloudy.

Stir the vanilla extract into the warm strained syrup, if using. Taste carefully and add another teaspoon of lemon juice only when a sharper flavor is preferred.

Let the syrup cool uncovered for about 45 minutes. It should be near room temperature before it is sealed or added to an iced drink.

Pour the cooled syrup into a clean glass jar or bottle. Seal tightly and refrigerate until ready to use. Start with 1 tablespoon per 8-ounce coffee drink and adjust to taste.