There's also Lapis, a really great and reasonably feature-full web app framework for OpenResty: http://leafo.net/lapis/. I wrote a website in it recently and was pleasantly surprised at how cool it is. It reminds me a lot of Rails, but everything works faster, especially on LuaJIT, and I actually like MoonScript (the compile-to-Lua language I'm using) for its expresiveness and aesthetics. Definitely recommend checking it out.

We use the lua support in openresty to build our authentication layer for admin tools outside of those admin tools. Very easy to integrate it with a third party authentication platform and just provide auth for free to our app developers.

That is not fully true.

It became a lot more true during 2013, but CloudFlare had already been operating for a few years then. A lot of fairly simple code was retired to the profit of Lua code, which is way easier to maintain.

There are still important modules written in C and compiled with Nginx. There are also proprietary extensions of the ngx_lua api to manipulate internal some internal aspects of Nginx within the scripts.

source: I wrote a good chunk of both iterations.