In a small saucepan, combine 1¼ cups of water, 1¼ cups of granulated sugar, and 12 chopped strawberries. Heat over medium until the mixture simmers gently, about 5 minutes. Stir occasionally to dissolve the sugar completely. Strain the mixture through a fine mesh sieve into a heat-safe container, discarding the solids.

In a large pitcher, combine 2½ cups of hulled strawberries with 3 tablespoons of sugar. Use a muddler or fork to gently mash the strawberries, releasing their juices. Let this mixture sit for 10 to 15 minutes.

Pour the cooled syrup into the pitcher with the macerated strawberries. Add the freshly squeezed lemon juice and about 4 cups of cold water, mixing gently until well combined.

Refrigerate the mixture for at least 30 minutes. Serve the lemonade over ice, garnished with lemon slices or additional strawberries.