In a saucepan over medium heat, combine 3 cups water and sugar. Stir until the sugar is dissolved and remove from the heat; set aside.
In the jar of a blender, add strawberries, 1 ½ cups water, and lime juice. Process until liquified.
Place a fine sieve over the saucepan and strain strawberry mixture; discard any seeds.
Pour the mixture into a pitcher and stir until nicely blended; taste and adjust if necessary. Refrigerate for at least 2 hours before serving over ice. Yields 6 ¾ cups.