What is the method used by Oomuro Sakurako in her "lucky color" lottery?
This is a method of randomly assigning things called "ghost leg" (in Japanese, called "Amidakuji", which means "Amida lottery"). 

Basically, the way it works is that each player picks one of the lines at the top. Then, you follow the line downwards. Every time you intersect a horizontal segment, you follow it. Here is an example of one possible outcome for a player of this game.



Note that the loop-de-loop and the non-strictly-horizontal cross-segments (like the ones that go left-down-right and right-down-left from the rightmost line) are not used in conventional ghost leg. This is just the show being silly.

This system is well-known in Japan (and maybe the rest of East Asia?), but is certainly not well-known elsewhere, which is likely why you have never heard of it.