First of all I want to say it’s not a matter of being compatible but more a question if Luminar 4 can be opened from the command line with a file parameter. The ‘export to/open with’ commands just send a text file to the command line containing the path and name of the program and the path and name of the file. I even can send it to OpenOffice.
Maybe a plugin mentioned by Patrick might be of a help.
You start from within LR and call PL. Your open a raw file from LR in PL. From PL you export it to LR as a jpg/tiff or what else. Now you have the exported file registered in LR in a specific way and you can call Luminar or which one you need. LR is functioning as a command center.
I don’t have LR so I didn’t try it but understanding from the reading it works like that.
George