If Photoshop and Lightroom are the same, the monitor profile is most likely fine, and they are both correct.
Eveerything else that is not the same, is not properly color managed and not correct.
When you don't know how it will be seen by others, it is particularly important that you do it right on your end. How other people choose to set up their systems, or what platform they want to use, is really not your problem, and there is very little reason to worry about it. Just do it right, and anyone out there who cares enough can take care of themselves. If they want to see it correctly, they can.
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