In a small saucepan over medium heat, combine the sugar and 1 cup water, stirring until the sugar fully dissolves and the liquid runs clear, about 3 minutes.
Remove the syrup from the heat and let it cool to room temperature, about 20 minutes.
In a large pitcher, combine the cooled syrup, fresh lemon juice and the 4 cups cold water, stirring to combine.
Add the green food coloring one drop at a time, stirring between drops, until the lemonade reaches a bright grass-green.
Refrigerate the base until cold, at least 1 hour, or make it up to 2 days ahead.
Just before serving, top with the chilled club soda and stir once, gently, so the bubbles hold.
Pour over ice and garnish each glass with a lemon wheel on the rim.
Good to Know
Make the syrup and lemon base up to 2 days ahead; the soda is the only thing that waits until serving time.