Have you drilled deeper into the CUI? I assume LT has a part for double-click actions? Under that you should find what Dean showed in his image. That should say what command would be invoked by double-clicking on MText.
I am wondering if you might not be referring to the action of MText that is part of a dimension. For some odd reason Autodesk changed the default to bring up the properties instead of the editor. I found in another post how ot change it back, but my details are sketchy. It involved duplicating one of the categories, changing it to dimensions, and redefining the double-click behavior to ddedit. Check the old posts from about 2 months ago. It came in very handy!
I hope my info was useful, but if by some odd chance it actually solved your issue, feel free to mark your post as "Accept as Solution". Thanks! 🙂