The reason that Lightroom does not auto-import your exported files is because the engineers designed the export feature to create consumable images, i.e. one time pics. They expect you to use the file (maybe printing at a lab) and re-export the files if you need them again in the future. Importing these exported files will not be a problem but you must make sure they have different filenames then your originals. You may then choose to stack them (if they exist in the same folder as the originals) if you like for a more fluid look in grid mode.
If you want to have files that you edited in Lightroom but send elsewhere they expect you to right click and click on Edit in PS. This creates a TIFF or PSD and can autostack with the original if you check the box. Then when you save the TIFF or PSD after additional editing LR will update the image in its database. However, if you do a Save As and save as a JPEG you still have to re-import the file.
Again, the Lightroom engineers designed LR with the expectation that you will only use LR to edit your files. If you use something else to edit them you will have to re-import the files.