Is it possible to rotate JPEG2000 quickly and losslessly without deep re-compression like it's possible for JPEG? Is there tool for this?
Using Imagemagick it is possible to specify lossless rotation:
> convert -rotate 90 -compression lossless source.jp2 destination.jp2
More information is available in the Imagemagick man pages. Whether it will be quick is a matter of how much hardware is thrown at the task and the definition of 'quickly'. I'd expect, but cannot confirm, that specifying lossless compression will indeed be lossless. It's probably a question for the Imagemagick Discourse Forum.
(I'm assuming you're using Windows, sorry if you aren't or your OS of choice doesn't have a similar application) Right click the picture, hover over "open with", select Windows photoviewer (not just photo) and it should open in the viewer; In the lower toolbar section, there should be circular arrows, click on the direction you wish to rotate. I'm not familiar with .JPG2000 images, but that should work. also, if you don't mind me asking, why do you use such an exotic image form? why not use .RAWs, .PNGs, and normal .JPGs?