Make the strawberry syrup: Combine strawberries, ½ cup water, and sugar in a saucepan over medium heat. Simmer for 10–15 minutes, mashing the berries slightly as they soften. Strain through a fine mesh sieve to remove seeds and pulp. Let cool.
Mix the lemonade: In a large pitcher, stir together the fresh lemon juice, cooled strawberry syrup, and 4 cups cold water. Mix well and taste. Add more sugar or water if needed.
Serve: Chill in the refrigerator or pour over ice. Garnish with sliced strawberries or lemon rounds if desired.