I’m thinking - if some kind of ‘white balance picker’ could be applied to the LUT.
How it could work: user picks a color, then RT will ’ color balance’ the LUT to that this selected color is the same on output as on input.
However this may/will destroy or hurt the ‘looks’ of the LUT. Remember the LUT is designed for example to create a faded look with shifted colors, you can’t correct that. And black and white… - no way that gets its color back!
I think my proposal thus is also impossible.
Another thought: you know that the CLUTs are easily editable, right? Open them, adjust (adding red for example) and save. And then you have a new CLUT with more red.
So my recommendation is: apply LUT, edit color to taste, save settings.
Then open LUT image, apply settings to it, and save new LUT.
Then you have a LUT that protects the colors you want.