I want to print a transparent PET bottle for my homemade lemonades and thought about 3D-printing them.

I would like the printed bottle's quality to be as fine as a Coca-Cola PET bottle for coke and the printing substrate or material be something that's cheap or readily available. I thought I might recycle some old PET bottles to print the custom one for my lemonades as I don't want something that would require me buying new materials or re-exporting from the manufacturer.

Is it possible to recycle PET and print it into food-certified containers?

No, due to 3 reasons

PET is not (easily) printable.

There is a lot of confusion on what Filaments you can buy: most times filament branded PET is actually PETG, sometimes PETT.

PET is not an easily printable material at all. With expert knowledge and the right machine settings it can be printed, but even then, it is not as easily recyclable into a useable 3D-printer-filament as you might think. You need full reprocessing capabilities, which means the need for machinery to allow thorough cleaning, grinding to dust, melting it up, pelletizing and finally extrusion as a fresh filament.

The closest related material that is easily printable is PETG, a modified PET that also contains glycol. You can't convert PET into PETG with home or hobbyist applications at all - they are totally different in their chemical behavior, even as just one material was added in production. PETG is not brittle like PET, it does not haze on heating, but it ages in UV light, scratches easily and can't be autoclaved like PET. But the chemical modification has to be done during the initial manufacturing of the material, and it is a huge mess to try to recycle the two together, which can and will happen if you try to work with material you source from recycling.

“When they’re processed together, PETG melts and becomes sticky while PET remains solid. PETG sticks to PET chips and forms large clumps that pose processing problems.” ^{Resource Recycling (magazine/blog)}

3D printed objects are very unlikely to become food certified.

You can't easily manufacture (certified) food-rated printed products, like food containers due to the requirements that a machine that manufactures food-certified products needs to comply to. I advice looking at this answer regarding food rating for more elaboration.

It is impossible to print really transparent with FDM.

Due to the method how FDM works - extruding lines next to each other - it is impossible to print fully transparent objects - there is always air inside a printed object, and there are so many boundaries between the extrusion paths that refract and change the photon paths that the best one can achieve is translucent (=semi-transparent). Read this answer for further information.