For LR ---? But is should act rather like Photoshop as both are by Adobe.
You retain Camera data in your EXIF when you do a Save As... If you do a "Save for Web", then I understand that you need to
tick a box somewhere to retain Camera Data in EXIF, otherwise just the Adobe actions are recorded in EXIF.
On top of that, some EXIF reading programs do give you a cut-down set of info, but usually that basic camera info is recorded.