As the topic is shown above, I have four presumptions are:

(1) LUT is a non-linear pixel data change protocol. It will correct or
modify the original pixel data before mapping pixel data to displaying
value via a color-map.

(2) Window level is a linear transforming protocol for pixel data to
display value. It will build up the details of the color-map that I
mentioned before.

(3) LUT can take above two changes together at once (non-linear, and
then linear).

(4) As a DICOM image, there must be a window level parameter. You could
have a LUT as well, but it is not the essential parameters in DICOM.

Please correct me if there is any misunderstanding in my presumptions.

I have a question as well:

Why most CT and MRI image does not contain LUT and only use window
level as the main image processing tool?