Add the sugar and lemon juice to a small bowl and stir together until the sugar is completely dissolved, this will take several minutes.

Add the lemon syrup, 2 cups water, and the chopped strawberries to the pitcher of a blender. Process until smooth, about 30 seconds on high. If you want to remove the strawberry seeds for a smoother paleta, strain this mixture through a fine mesh sieve. If you don't mind leaving the seeds, continue to step 3.

Pour strawberry mixture into 10 popsicle molds, insert sticks, and freeze until solid, at least 6 hours.