For the thyme and lemongrass syrup, put 600ml/1pint of water into a saucepan and add the sugar, lemongrass and thyme. Bring to the boil and simmer gently for 10 minutes. Remove the pan from the heat and set aside to cool.
For the cocktail, squeeze the lime wedge into a tumbler. Add the gin, lemongrass syrup, top up with tonic water and stir gently. Garnish with a sprig of fresh thyme.