> Mention me a _serious_ operating system using lua on their kernel side and I'll acknowledge that last sentence.

NetBSD, of course.

> Be sure we are talking on the same page, we are talking on the context of being used for programming operating systems, is lua mature for that domain?

As https://www.lua.org/about.html notes,

> Lua is embeddable

Lua is specifically designed to be embedded into other things in order to make them easily extensible.