Today, after a long time away (and because Neverwinter is down for maintenance) I fired up Lord of the Rings Online to kill a few orcs. I was greeted by an update which then led to the loader not being able to find its own client executable. Some digging around on Google led to an article about how none of the games files can run as Administrator, and that this often causes this error. I checked all of mine and none of them were. A bit more digging led to this article:

• The new launcher is asking “Where is the client executable?”

This article was dated two days ago, and the steps outlined solved my problem. I post it here for any others who might run into the same issue.