Tool for lossless rotation of images
The only true lossless rotation for images would be a file format that allows you to save the image in its original format, and then specify what angle it will be rotated to when displayed on screen.
One program which can do this is InkScape. It will allow you to import (and embed) an image, and then rotate it. You can then rotate the image to any angle, as many times as you like without causing any loss of quality.