Add 1 cup of water and the sugar to a medium-sized saucepan. Bring to a simmer over medium heat, stirring occasionally, until the mixture turns into a transparent syrup (you should be able to see the bottom of the pan), 6-8 minutes. Chill in the refrigerator until cool. You can speed up the process by placing the syrup in the freezer.
5 cups cold water, 1 cup granulated sugar
Puree the strawberries with 1 cup of water in a blender until smooth.
2 cups strawberries
Strain the strawberry puree through a fine mesh strainer, pressing with a spatula to extract the juices.
Add the chilled simple syrup, lemon juice and strawberry puree to a pitcher, stirring to combine. Add the remaining 3 cups water, or more to taste.
1 cup fresh-squeezed lemon juice
Pour over ice to serve, garnishing with lemon slices and or strawberries if desired.