In a non-reactive bowl stir together the lime juice and sugar until sugar is completely dissolved. Wet the rims of serving glasses with water and dip in sugar, set aside. Combine the lime syrup and all remaining ingredients in a blender and process on high speed until completely smooth, 2 to 3 minutes.
Serve in sugared glasses, garnished with lime slices.
Recipe courtesy of Emeril Lagasse, 2005