Adding lemon rind to the sugar syrup gives an extra bit of flavor.
In a small saucepan, combine sugar, 1/2 cup water, and a few pieces of lemon rind (yellow part only). Bring to a boil and remove from heat.
Squeeze lemons and combine juice with sugar syrup, vanilla, and remaining cold water.
Add ice and serve in tall glasses.
We used Meyer lemons, which are sweeter than regular lemons.