Both of the histograms are from Lr. The photo was opened in Lr and then brought into Ps via Edit In option, and then saved and brought back into Lr. So the histogram should be the same in both files. Sorry for any confusion.
There is no need for that, it's just a very common misunderstanding. Any profile will be correctly handled in Photoshop.
If there is a difference between them, the usual cause is a defective monitor profile. As a diagnostic test, try to replace your current profile with sRGB IEC61966-2.1. Relaunch both applications when done, the profile is loaded at application startup:
If that clears it, you should use a calibrator to make a new monitor profile.
And if that doesn't fix it, there are some more obscure problems. If you are using custom/third party camera profiles, there is a bug that prevents the profile from being correctly transferred from Lightroom to ACR/Photoshop. The native/standard profiles are not affected by this.
Finally, if you're using very old Lr/Photoshop versions, it can be a version mismatch, again causing problems with camera profile handling.
The error exists regardess of which color profile I set for the monitor. As per your suggestion, I've tried the srgb and default profiles to confirm. My current calibration is usiong iDisplay software. All software is up to the latest verions.