Make Strawberry Syrup: In a medium saucepan, combine sliced strawberries, ½ cup sugar, and ½ cup water. Simmer over medium heat for 5-7 minutes until strawberries are soft and broken down.
Puree and Strain: Remove from heat, let cool slightly, then blend until smooth. Strain through a fine-mesh sieve to remove seeds.
Juice Lemons: While syrup cools, juice lemons to yield 1 cup of fresh lemon juice.
Combine Ingredients: In a large pitcher, combine strawberry syrup and fresh lemon juice.
Add Water and Sweeten: Add 4-5 cups of cold water, starting with 4 cups and adjusting to taste. Add remaining sugar dissolved in warm water if more sweetness is needed.
Chill: Refrigerate for at least 30 minutes to allow flavors to meld together.
Serve: Pour over ice in glasses, garnish with fresh strawberry slices, lemon wheels, and mint leaves