Roll lemons on the counter to soften, then halve and juice until you have 1 cup (240 ml) fresh lemon juice.
Strain the lemon juice through a fine sieve to remove seeds and excess pulp.
In a small saucepan combine 1 cup sugar and 1 cup water; heat gently, stirring until the sugar dissolves to make simple syrup.
Allow the simple syrup to cool to room temperature before mixing.
In a large pitcher combine the strained lemon juice and the cooled simple syrup.
Add 3–4 cups cold water to the pitcher and stir; taste and adjust with more water if the lemonade is too strong.
Add ice cubes to chill quickly or refrigerate the pitcher for about 30 minutes before serving.
For a sparkling version, replace part of the still water with chilled sparkling water just before serving.
Garnish glasses with lemon slices and fresh mint sprigs if desired.
Serve over ice and enjoy immediately for the best, freshest flavor.