Infused Simple Syrup: In a saucepan over medium heat, combine the sugar, water, cilantro, mint, basil, and crushed lemongrass. Slowly bring to a simmer and cook until the sugar is dissolved. Take off heat and let herbs steep until the liquid is cool. Strain into a glass or a bowl and reserve.
Cucumber Juice: Add the cucumber to a blender with 2 cups of water. Blend on high until fully liquefied, then pour through a fine strainer and reserve.
Drink: Add the drink ingredients to each pint glass filled with ice. Stir and garnish each glass with a cucumber stick and a lemon slice.