Busted: elegant unit testing for Lua
olivinelabs.com
olivinelabs.com
busted is inspired by frameworks like Mocha and Jasmine, and comes bundled with support to easily change the output functionality, write your own asserts, chain and negate asserts, and integrates an i18n library so that you can customize the language in the output. It installs using the luarocks package manager.
When learning you should read PiL (Programming in Lua)
I can't speak for everyone else, but in my experience the reference manual is quite complete, and Programming in Lua is perhaps one of the best technical books I've ever read when it comes to concision and clarity.
But documentation of 3rd party Lua modules is substandard, if I compare them to CPAN.
The Lua reference manual is, I think, a pretty good reference manual. It's quite complete, well-indexed, and reasonably well organized.
If you're simply annoyed by having to page through the index to look for a function, you can try the search-based version of the reference manual, at http://pgl.yoyo.org/luai/i/about
The reference manual is, however, a reference manual, and doesn't have much in the way of a high-level overview of various features, or examples. For those things, PiL ("Programming in Lua") is a much better resource. The latest version of PiL is a real you-gotta-pay-money book, but a slightly older version is available online. For both info about the book, and the online version, see http://www.lua.org/pil/