The simplest approach is to use a display of known colour space - say Rec709 - and then look at a known image through the LUT.
The image needs to be from a source the LUT was made to work with - images from the camera used on the production.
You will quickly be able to tell if the images look correct or not.
If for a P3 display the images on the Rec709 display will look over saturated.
You can then use LightSpace CMS to concatenate the LUT you have with a P3 to Rec709 LUT to correct the LUT.
Mob Boss at Light Illusion