Tried a few experiments with Lightroom / Photoshop…….
1. If you delete a photo using say File Explorer / Bridge / Photoshop etc, Lightroom will NOT detect that unless you Synchronise the Catalogue for the folder it was in. You could carry on developing the image quite happily but of course when you came ot export that would fail.
2. If you bypass Lightroom and use the Photoshop Raw editor then those changes will NOT be reflected in Lightroom until you Sync.
3. In Lightroom Edit / Catalogue Settings / Metadata tick ‘Automatically write changes into XMP’ and Lightroom will create an XMP file if you develop that photo. Now detects file is missing is you try and develop it having previously deleted in step 1 above but…………
4. Having done step 3 I would have thought changes done in Lightroom would be reflected in Photoshop. That is NOT the case unless you launch Photoshop from within Lightroom while editing the image there.
Moral of the story :- If you use Lightroom ( which I think is the best way to manage editing workflow ) then you must use it as the master or ensure you Sync folders if you break that rule.