I follow the basic lemonade recipe; making sugar syrup and adding it to lemon juice. The result is perfect but when I leave it overnight in a bottle it seems like the juice (or a white substance) sinks at the bottom and every time I want to drink I have to shake the bottle. Is there any way to prevent that from happening?I want to make fermented lemonade and it will be impossible to shake the bottle because of the carbonation.
You could clarify your lemon juice/lemonade, then ferment it. This would eliminate any precipitates. The agar clarification process is fairly straightforward, though it takes some time. Agar can be purchased fairly easily. I've achieved the best yield with the freeze/thaw method. Of course, if you have access to a centrifuge, that would be the best option.
Similar cloudy lemonades are available commercially here, and the sediment in those can be mixed back in by gently inverting the bottle a couple of times then pouring into a glass. There's no need to shake and this no problem from the carbonation. It works best if you're pouring out the entire bottle in one go.
So depending on how you plan to bottle it, you might not have an issue.