Did you use linked or embedded Smart Objects?
Well, I'm not sure what the difference is. I edit a RAW file in Lightroom and open it as Smart Object in Lightroom.
Also, I could open the RAW in Bridge, but they might be edited in Lightroom.
So I use the original RAW file that mostly is edited in Lightroom as a start.
In this case, will Camera Raw influence the edit I made in Lightroom or is the edit 'on his own'?
If you open the image as a Smart Object from Lightroom, the image will be sent to Photoshop as a Tiff file. If you double click that layer it will open in Camera Raw, but all the settings will be their defaults because as far as Camera Raw is concerned, this is a brand new image. None of the changes made will affect the RAW changes you made in Lightroom since you are now effectively working on a copy of the original image.
It's a bit more complicated if you open the image from Bridge. Bridge sends the original RAW file to Photoshop when you ask Camera Raw. If you double click the smart object, all the Camera Raw settings will be set just as they were when you opened it from bridge. At this point, any changes you make WILL be reflected in the original RAW file right up until you save the file in Photoshop. Once Photoshop has saved the image, changes made to the Smart Object will no longer show up in the RAW file if you re-open it in Bridge or Lightroom.
Once you have saved a file in Photoshop opened from Bridge, it works the same as Lightroom with one important exception. Opening from Bridge retains all the settings you made, so you can undo them (without affecting the original image). If you open the image from Lightroom, you can no longer undo the settings made in Lightroom from within Photoshop without starting all over. So for example, if you set the image to +10 exposure, open it from Lightroom and then open the Smart Object, ACR will show the exposure as 0. You could make it -10 to compensate, but you will lose information in the photo. From Bridge, if you open the Smart Object, ACR will show the exposure as +10 so you can undo it with no loss of information.