I work for/with/teach pro colorists. Looking at your post, I have immediate ... questions.
LUTs are not math ... they're simple look-up tables ... charts ... which apps use to manually drag this RGB triplicate to that. There are a few given ... (the number of points) ... and in between those, the app simply does typically a straight-line mod.
LUTs are fixed value tools. So if your image is exposed either lower or higher than the LUT was built for, you will get crushed shadows or clipped highlights. So great care is required.
Which is why colorists basically never apply a LUT of any type without being able to trim the clip into the LUT to keep from getting crushed, clipped, or over-saturated values.
In Premiere there are a couple ways to do this safely. The easiest is using the Creative tab slot to apply the LUT, then doing the image trimming in the Basic tab.
The other is by stacking multiple Lumetri ... the second instance with the LUT applied in the Basic tab Input slot, and using the first instance of Lumetri to trim the image.
Auto-color and Auto-match in Lumetri
There are two automated tools for color ... I'm faster manually than using these, but many less-skilled workers love them.
Auto-color in the Basic tab (if I recall correctly!) ... click that, and it tries to make the image as "normal" as possible. Sometimes, it does a nice job.
Auto-Match Color in the Color Wheels tab of Lumetri.
- Set the first clip color as you wish it to look;
- Set Lumetri into Comparison mode;
- move to the next clip, select a good frame, and click auto-match.
This can, when selecting a pretty close apples to apples pair of images, do a pretty decent job.