I could install the NIK 3 applications as plugins in Photoshop 2021 without problems. That isnot the case in Light Room Classic 2021. Since weeks I’m looking for a solution. From DXO support not many reaction AND NO SOLUTION TILL NOW
Bienvenue chez nous Roger. 
I guess that your installation of the Adobes is standard. Is your OS Windows or Mac ?
When you installed the Niks, did you notice if Lightroom was detected ?
I guess that you know where you should find the plugins in LrC : right click on the photo and the “Edit in” for most of them. HDR efex is different : File > Export with presets > DXO > HDR Efex Pro 2.
I use LRC 2021 on a macbook pro 2020 with OSX Catalina. With more than enough power.
Yes i saw during install that LRC was detected.
Using the “preferences system” to install plugins from LRC brings me ONE plugin UNDER the plugin Edit with Photoshop… and not in the list of other plugins as Luminar AI.
As soon as i install a second Nik plugin the fist one is overwritten there…
With the Adobe support taking over my screen we try during many many time to find a solution… without result… i did it twice with 2 different support people…
Reinstalling a blank new LRC was also not a solution because i got the same result
I’m hopeless.
Thank you if you can help me
Roger
Belgium