When Photoshop Lightroom starts, it checks to see if Photoshop is installed. If it can't find Photoshop, it checks to see if Photoshop Elements is installed. If it can't find either, Photoshop Lightroom disables the Edit In Photoshop command. The Additional External Editor command is not affected.
If you uninstall an older version of Photoshop after installing a newer version, some of the data required for Edit In Photoshop could have been removed. Reinstalling the latest version repairs this issue.
On Windows, Photoshop Lightroom checks for the Photoshop.exe or PhotoshopElementsEditor.exe keys in the HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\App Paths\ directory of the registry. These keys provide the file path to the applications.
On Mac OS, Photoshop Lightroom checks for the com.adobe.Photoshop.plist or com.adobe.Photoshop.Elements.plist files in the user's preferences folder. These files provide the file path to the applications, as well as other OS-related information about the applications. The plist files on Mac OS are created when you start applications for the first time. The files are also created any time the application is started and the files are not present.