The first look-up table effect that really impressed me was to use them for making a textured tunnel.

You have a look-up table such that for each pixel on the screen, you know its angle and distance from the center of the screen. With this you can pick which texel to put at each pixel location.

It looks as if you are moving in a tunnel with 3D geometry, but it's so cheap you can even do it on pico: https://www.lexaloffle.com/bbs/?pid=63818

At first I thought the game Stardust must have used this effect, but reading up on it just now they actually just play a repeating 6 frame animation for the background! https://codetapper.com/amiga/sprite-tricks/stardust/