LRC --> PS --> LRC import ISSUES

Besides making sure that you check alongside the starting image in its Folder view - and with any filtering disabled, for example if you are viewing only Raw format images - there are a couple of technical matters at the Photoshop end.

Firstly to exclude this: once you have initially saved the image from PS, further saves of variations under a different name will not be automatically seen by the Catalog. 

Next, PS has a setting to 'Include Compatibility Preview'. This applies for PSD - since TIFF includes one regardless. Un-checking this option means a PSD will save slightly smaller when it has got layers - but the consequence is, any PSD which is layered will then become unreadable by Lightroom / LrClassic (though a flat file - only a Background layer - would be readable). So this option needs its checkmark.

Next: LrC is looking for a standard RGB format file, or else can interpret (and internally convert to RGB for its own operations) a CMYK format file. But setting any other colour-model options such as Duotone, will IIRC make that file a mystery to Lightroom. 

Configuring LrC's external editing to happen in TIFF file format is perfectly fine, and supports everything (such as Smart Object workflow) that PSD would otherwise support. But at the PS end, I would not set the compression options for TIFF to anything unusual in case LrC might then have difficulty unpacking that.

Also - depending on operating system - both PS and LrC may need to be granted full modification rights to the file system.

Also: if your file system is being synced to cloud - for example, if OneDrive is backing up Pictures and this is where the image file is being made - there may be a temporary lock while the newly made file is being synced online, getting in the way of LrC's import of that as a new image. This could be sporadic and accidental. Personally I am not a fan of continually syncing, live, any area of the file system that the Catalog is also constantly managing, in potential competition with the syncing operations. 

I am sure there are further considerations but - those are the ones that occur to me right now.

Are you looking for the images when you are in a collection?

What steps do you follow to go from LrC to PS? Please be specific and detailed, leaving nothing out.

What steps do you follow to go from PS to LrC? Please be specific and detailed, leaving nothing out.