A quick search suggests to me that it's only a lossless process if the image dimensions are a clean integer multiple of 8 or 16 (as the blocks can be 8x8, 8x16, 16x8, or 16x16), otherwise the edges must be reencoded. Never written a JPEG codec though, so happy to be proven wrong.

This is true, and others have mentioned it, but I think people are underestimating just how universal sensor dimensions being a multiple of 16 is — I really can’t think of any exceptions.