For the lemon syrup:
1 ½ cups sugar
1 cup water
1 ¼ cups lemon juice (5 to 6 large fresh lemons)
Squeeze lemons over bowl, keeping juice, pulp, and seeds. Set aside the peel of one lemon, yellow part only.
In a saucepan, combine sugar, water, and a few drops of lemon juice, and bring to a boil. Simmer over moderately low heat, stirring, until the sugar dissolves. Pour the syrup into a heatproof bowl and let cool to room temperature, then stir in lemon juice. Add lemon peel, cut into fine slivers. Store in a bottle in the refrigerator.
Prepare the limonata:
In a glass, place some ice and pour over lemon syrup and fizzy water, one part lemon to four parts fizzy water (or to taste). If you wish, serve with a slice of lemon.