In a small saucepan, combine sugar and 1 cup water. Bring to boil and stir to dissolve sugar. Allow to cool to room temperature, then cover and refrigerate until chilled.
Remove seeds from lemon juice with a spoon, but leave pulp. In pitcher, stir together chilled syrup, lemon juice and remaining 3 cups water. Serve over ice cubes and enjoy with a wedge of lemon or lime.