When Lightroom starts up, it checks to see whether Photoshop or Photoshop Elements are installed, and if it can’t find them, then the Edit in Photoshop menu command is disabled.
If you install a new version of Photoshop, and then uninstall an earlier version, the link can get broken by the uninstall. Uninstalling and reinstalling Photoshop will usually solve it, or you can fix it by editing the registry key (Windows) or deleting Photoshop’s plist file (Mac). There’s more information on the official Adobe tech note at:
Of course, you may be able to take the easy course and add it as an Additional External Editor, however you would be missing out on some of the direct integration which comes with matching ACR versions. We’ll go into detail in the next question.