A display LUT is an array of 256 (or 2N) entries, each holding an RGB triplet. Each pixel's intensity indexes the array and returns that pixel's display color. Linear LUTs map proportionally (green: 0→black, 255→bright green). Non-linear LUTs such as 'Fire' use multi-segment color ramps to enhance contrast in particular intensity ranges.
A display LUT does not modify the stored pixel values. Quantitative measurements are always made on the raw intensity data, never on the false-color display.