Does Lightroom 5 do any lossless operations on JPEGs?

There are many lossless transformations that can be done on JPEGs:

1. Crop


2. Rotate by 90 or 180 degrees in either direction


3. Flip horizontally or vertically


4. Transpose along either diagonal axis


5. Modify only a small area of an image, and save the JPEG, while recompressing only that small part of the image.

Does Lightroom 5 support any of these? I can use another app, but I'd rather use Lightroom, so that I'll have the entire history of the edits and can undo or tweak them months or years later.

References: JPEGtran and GraphicsMill.

Answer

In general these operations are simply not possible to perform losslessly on a JPEG. Rotations are only mathematically possible when both the height and width of the JPEG are multiples of 8 or 16 pixels depending on chroma subsampling. You can read more about it here and here. If a website claims something else it's simply not true.

Regarding the other operations they are limited to the same constraints as explained in the links, the MCU:s (Minimum Coded Unit).

I'm not sure if Lightroom is capable of doing any of these operations even if and when they are mathematically possible, but if you're worried about how the program handles the problems and limitations that is a result of the architecture and design of the JPEG standard you're using the wrong format. Switch to RAW and transform it however you like and as a very last step export to JPEG as a finalised file and you won't have to deal with these problems at all.