Place ginger into the Thermomix bowl and mill 6 sec/speed 6.
Add water, and sugar and boil 15 min/100°C/speed 2/spatter guard.
Allow to come to room temperature completely before proceeding. This will take up to several hours if left in the Thermomix bowl. If you want to speed the process up, remove from the TM bowl and cool in another bowl. If you want a more gingery taste, simply add more ginger in this early stage.
Strain the mixture. Add the lemon juice and ginger bug and stir 10 sec/speed 5 or stir well manually.
Pour into sterilised bottles with a flip top. These are widely available at Kmart, on Amazon or at Kitchen supply stores. You must not fill to the top. You should leave at least 2 inches of space at the top of the bottle for the gas to have room and to avoid explosions. If you want a sweeter drink, add a tsp of stevia to each bottle before sealing. Shake well.
Leave the bottle sealed at room temperature for a few days, 'burping' the lids every day. By day 3 or 4 you should have some bubbles happening.
You can now refrigerate the bottles and start drinking them. (No need to burp the lids once they are refrigerated.)
Disclaimer: brewing probiotic beverages at home can be risky. When fermenting probiotic foods and beverages, use caution. Always use well washed tools and when in doubt, throw it out! If you notice any strange smells or mold, be sure to discard the whole batch.