A mismatch in colors between Lightroom and Photoshop is usually due to either a corrupted or incompatible monitor profile or incorrect color space settings. For example, a ProPhoto RGB photo mistakenly rendered as sRGB will display as desaturated and flat.
ProPhoto RGB photo correctly displayed as ProPhoto RGB:
ProPhoto RGB photo incorrectly displayed as if sRGB:
The corrupted monitor profile is very easy to check, and there are instructions here.
We’ll also need to confirm that the color spaces match across the 2 programs. The same principles will also apply to opening photos in other software, not just in Photoshop.
First, check your color settings.
In Photoshop, go to Edit menu > Color Settings to view the Color Settings dialog.
The RGB Working Space is your choice, but whichever you choose to use, you’re best to set the same in Lightroom’s External Editor preferences and Export dialog. We’ll come to that in a moment.
Selecting Preserve Embedded Profiles and/or checking the Ask When Opening for Profile Mismatches in that same dialog will help prevent any profile mismatches. Preserve Embedded Profiles tells Photoshop to use the profile embedded in the file regardless of whether it matches your usual working space. Ask When Opening for profile mismatches shows you a warning dialog when the embedded profile doesn’t match your usual working space, and asks you what to do. If Preserve Embedded Profile is selected, you can safely leave the two Profile Mismatch checkboxes unchecked.
Then you need to set your External Editor settings in the Lightroom Preferences dialog > External Editing tab, and select the same color space that you’ve selected in Photoshop.
You’ll also want to check the color space that you’re using in the Export dialog, and again, if passing those photos to Photoshop, select the same color space for photos you’re going to edit in Photoshop.
As long as your Photoshop and Lightroom color settings match, or you have Photoshop set to use the embedded profile, your photos should match between both programs.