Have you tried temporarily disconnecting the thunderbolt or USB cable for the backup drive? Does that make any difference?
Hi and thanks for getting back to me so quickly. I've just tried temporarily disconnecting the cable for the external drive but still got the same error ("the files could not be edited because Photoshop CS6 could not be launched").
If I delete the com.adobe.Photoshop.plist file, then close and relaunch Lightroom with the external drive disconnected, it will run the version of Photoshop on my boot drive. I thought for a moment it was fixed, but when I reconnect the external drive it goes back to trying to run the backup version of Photoshop on that. Unfortunately I need to keep the backup drive connected as I back up my work at regular invervals throughout the day and there is a second partition on the same external drive which contains many of my image files.
Thanks and best wishes,Anna
After posting this question I tracked down the answer myself - it seems that this is a bug in Lightroom which Adobe have known about since at least January 2015. As far as I know it hasn't been resolved in the latest version of Lightroom, but they have written a plugin which gets around the problem. I've downloaded and run it and it works, so I thought I'd include the link to the page in case anyone else is having the same problem:
Ignore the first suggestion about uninstalling Lightroom and Photoshop and scroll down the page until you find the official response from Jeffrey Tranberry - there's a link to download a plugin there and once you've installed that you'll be able to specify the location of Photoshop. With any luck the problem will be fixed properly in a future version of Lightroom.