I am using both PSE 13 and Lightroom 5. When I use Lightroom as an external editor and save the photo, it shows up in PSE13 as an edited file but does not look any different. Why doesn't it appear edited?

Question

I am using both PSE 13 and Lightroom 5.  When I use Lightroom as an external editor and save the photo, it shows up in PSE13 as an edited file but does not look any different.  Why doesn't it appear edited?

Answer 1

People who have Photoshop, but don't have Lightroom, need ACR so that they can use Raw files. Without ACR they could do nothing with those (they may also like having ACR so that they can work on other kinds of image using the same kinds of adjustments and techniques, as are used with Raw files).
People who have Lightroom, can get access to Raw files regardless whether ACR is present or not. They can use Lightroom on other kinds of image also, using the same methods. LR can pass images directly into Photoshop without passing via ACR (or else does so transparently, which amounts to substantially the same thing).
ACR does not, strictly speaking, even need to be installed for this external editing to happen. In fact, not even PS needs to be - since a different image editor can be used instead, while still retaining the Adobe Raw conversion etc.
Lightroom "subcontracts out" specialised external tasks, in this workflow, but is still your "main contractor": the image is otherwise located, viewed, managed, adjusted/presented and output entirely using LR.
So IMO we can divide image processing into:
operations that involve pixels and layers and layer masks and adjustment layers etc (of the kind done inside Photoshop)
operations that involve parametric edits (of the kind done in ACR where you are not using a Lightroom based workflow; otherwise, done inside Lightroom)
When PS is called in, that's because those tasks are impossible or unsuitable to do in Lightroom. But those tasks can't be done in ACR either - by definition, since LR and ACR have exactly the same image processing "feature set".
Lightroom is irrelevant to the Bridge + ACR + PS workflow. This workflow requires both your PS and your ACR to be current enough, to support your Raw format etc.
ACR and Bridge are irrelevant to the LR + (image editor) workflow. It is in this case, only LR which needs to be current enough to support your Raw format etc.
RP