Make the simple syrup: In a small saucepan, combine the sugar, basil, and water. Bring to a boil over medium-high heat. Once boiling, cook for 2-3 minutes, until the sugar has dissolved and the basil is fragrant. Remove from the heat.
Strain the herb syrup through a fine-mesh sieve set over a blender. Add the blueberries and lemon juice. Blend on high speed until smooth.
Divide the mixture between 6 ice pop molds. Freeze until solid, at least 6 hours.