The Pro Photo colourspace has many problems associated with it. It is a very wide gamut profile - so much so that no existing display device cannot actually display the range of colours in contains. As such, it's fairly hard to predict what will happen if it is badly converted to other colourspaces. Despite what Mr Evening says about it, there is almost no advantage in its use, and unless you really know what you are doing with it, can lead to more problems than it solves. The main reason I advocate not using it, is simply because no device you have can actually display it correctly.
Having said that, I don't think this is your problem. It's almost certainly a colour profiling mismatch between LR and Photoshop. What are your colour conversion policies set to in Photoshop?
If you wish to continue using Pro Photo, then you need Photoshop set up like this...
Pay particular attention to the tick boxes that dictate what happens when you have a profile mismatch or missing profile.
Another possible reason is you have calibrated your monitor and generated a V4.0 ICC profile, and you're on a Windows based machine. If so, recalibrate, but set your calibration software to generate a V2.0 ICC profile.
There's no reason whatsoever why you'd need to use ARGB. It is nothing to do with studio lights or it would just be as wrong in LR. If it's correct in LR, but incorrect in PS, then it can only be how PS is handling the embedded colour profile. Ensure ProPhoto RGB is your default working space.
As for black and white, you can still get odd colour casts with incorrect profile management, if it's still an RGB file. By B&W you probably mean you've just removed the colour, but it's still an RGB file. A true black and white image would be grey scale.
