Combine the sugar and 1/3 cup water in a microwave-safe glass measuring cup. Microwave until steaming, 45 seconds to 1 minute. Stir to dissolve the sugar.
Stir in the lemon zest and lemon juice, and set aside to cool completely. Strain through a fine-mesh sieve. (The lemon syrup can be made ahead and stored for up to a week in the refrigerator.)
To serve, fill a pint glass with ice. Add the sherry and 5 tablespoons of the lemon syrup. Shake until well chilled, then strain into cordial glasses. Serve cold.
Leftover lemon syrup can combined to taste with sparkling water for a fizzy lemonade.