[Here's a concise synthesis of previous posts and my own testing]
When you edit a raw photo in Photoshop that has a creative profile containing a LUT, Photoshop loses the profile. A workaround is to do Metadata > Save Metadata To File right before editing in Photoshop, or alternatively, set the option Catalog Settings > Metadata > Automatically Write Changes Into XMP.
To reproduce:
1. Make sure Photoshop is not running.
2. In LR, uncheck the option Catalog Settings > Metadata > Auto
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