Unfortunately, looks like the files in this category (Discussions) are not downloadable. So to test it as good as possible, I clicked on each image and did a screen capture of the image. At least that way I know the colors posted will be the same as presented on the screen.
I took those four screen captures, loaded them into Photoshop as Layers. I then aligned them to take care of any minor differences based on my screen captures. Here is the resulting Layer stack
Note in this .screen shot that the bottom two layers are currently not visible with the eyeball icon turned off.
Now I change the top layer blending mode to Difference. That will show any differences between that top layer (PS - SRGB) and the layer below it (LR - SRGB).
Here is the result:
You see the top layer blend mode is difference and the resulting image on screen is completely black. The tiny white line at the top is simply a result of alignment of the two layers based on my screen capture. The completely black image says there is NO DIFFERENCE between the PS - SRGB image the LR-SRGB Image.
To avoid this reply being too long, I did the same thing with different pairs of layers. I won’t post screen captures of every result because they look just like this one.
Compared the two ProPhoto images - Same Result - NO DIFFERENCE
Compared the the two LR Images - Same Result - NO DIFFERENCE
Compared the two PS Images - Same Result - NO DIFFERENCE.
So… my conclusion is that all four images are the same.
If you want to try the same thing with the exported images that you have rather than introducing the step that I had to do with screen captures, I’m guessing you are going to see the same result.
Try it, and post the results here.