Place ginger into the Thermomix bowl and chop 3 sec/speed 5. Add the water and cook 8 min/80°C/Reverse/speed 1. Allow to infuse in the bowl until cooled.
Strain well and rinse the Thermomix bowl out. Return the mixture to the bowl and add sugar. Cook 4 min/80°C/speed 1. Cool before adding lemon juice. Keep this mixture in a sterilised jar in the fridge.
To serve, splash some ginger syrup into a glass over ice, top up with sparkling water and serve with lime and lemon slices.