What are your color settings in Photoshop? The color management policies should all be set to "Preserve Embedded Profiles." You should also NOT have checked "Desaturate Monitor colors by 20%." The rest of the settings is not so relevant in general. Lightroom's external editing should just be left at the default (TIFF, 16 bit prophotoRGB, 240ppi and ZIP compression) except when you have an exceptional need. That is not the cause of any color discrepancies.
One of the major causes of color inconsistencies is bad monitor profiles. How are you calibrating your monitor? If you are not calibrating and you run Windows, the cause is almost invariably a bad monitor profile installed by a driver plugin. Macs don't have this issue fortunately but can have bad monitor profiles due to other reasons. The solution is to recalibrate your monitor. If you don't own a calibrator, go into your monitor's properties pane and delete any profile you see associated with the monitor. Then go to your favorite online retailer and order a calibrator. Both Windows and Macs have a built in calibration tool but it is not very good. There is no substitute for hardware calibration.
Thanks for you answer! Where do I find the colour management policies?
It's in the Edit menu in the "Color Settings" option. Generally if you choose a preset such as "North American General Purpose" or the Europe/Asia variant you should be OK. That should set all the policies to "preserve". Do NOT ever select "Monitor Color". That would cause major color problems.