Okay. I think my problem is solved. In my mind, exiting TG and then rerunning it was forcing TG to reload the model. But this is not so. TG "loads" the model and, apparently stores object along with the scene file when you save it. So simply rerunning the scene containing an instance of the object means that TG never looks at the mtl file again. You have to delete the object within TG and then reinsert it again. To be safe, after deleting the object from TG I inserted a different version of the object from a different file and the textures show up properly. I then went back and did the same thing using the absolute paths (with preceding slashes) and the textures show up properly. In the original cabin scene, I didn't want to actually delete the object because I would have lost all of the orientation parameters associated with positioning the object. And I didn't want to insert another instance of the object to copy orientation parameters over before deleting the first instance being afraid that TG would recognize it was coming from the same file and use cached parameters instead of forcing a reload of the same object. So I exited TGand reran it thinking that it would reload the object. But it does not. Now I think I understand what I was doing wrong. My mental model of that part of TG was flawed.
Another thing this clarifies is, since the object is not reloaded simply by rerunning a TG scene that already contains a non-textured object, it stands to reason that an error message would not be generated because a "reload" of the object isn't being done. But I did force a reload of an object that has an mtl file with the absolute paths generated by Lightwave that lack a preceding slash in the path name. TG does not find the image files but also does not report any error. So when I originally loaded the object that had an mtl file with absolute path names that needed to be manually repaired, TG just threw the textures out and recorded that there aren't any textures associated with the object. My TG scene has been carrying that same object through all my tests because I didn't actually delete and reload the object during the whole process.
From now on, after I have generated an obj file using Lightwave or Modo, I will have to edit the preceding slashes into the mtl texture file path names before I insert the object into the TG scene. If I remember to do this I thing I will be okay. This may even clear up a mystery problem that some TG users had long ago and have given up on Lightwave or Modo altogether for model creation thinking that they are generating flawed obj files when they are probably not. Editing the mtl files is really pretty easy. It just has to be done if you want to use either Lightwave or Modo to make your own models.
Problem solved and thanks all for the support. You were all great!
A question I have for Jo is: "If you don't delete the object from the scene I sent you but you do edit the mtl file in the way you describe (file only, no path) then do you see the untextured model when you run TG as I did?" If so then it clarifies things a bit more for me.