In a small saucepan, combine sugar and ½ cup water over low heat, stirring until the sugar dissolves. Don’t let it boil.
Add strawberries to the syrup and simmer gently for 2–3 minutes until they soften. Remove from heat and let cool slightly.
Strain the strawberry syrup through a mesh sieve into a pitcher, pressing on the solids to extract flavor, discarding the seeds.
Stir in the fresh lemon juice and 3 cups cold water, then taste and adjust: add more water if it’s too strong, or a bit more syrup if it’s too tart.
Add ice cubes, stir, and garnish with lemon slices or strawberry slices before serving.