Lua's design assumes you're comfortable with C. Lua in isolation has a library problem, yes, but in exchange can be small enough a language to learn and know in its entirety.
Many/most libraries in Python are built in, so you don't need to hunt them down and install. More importantly your users need only have "Python", nothing more or less and don't have to fiddle to get things working.
But unlike Python, Lua is smaller than SQLite. You can just put it in a DLL and install it with your project. Any users that even notice it would be shocked to see how many installations of SQLite they probably have. :)
I would expand that to say that lua has a standard library and framework problem. You can link any old C library but there's little uniformity in how everything fits together and rather few task-oriented packages/frameworks exist.
I like lua and am using it for some tasks where I'd have used C in the past. But for many things where ruby/python have strong, pluggable libraries (e.g. everything web-related) there is simply no equivalent in lua-land.
Lua's historical niche has been as an extension language for C and C++ projects, not web development. It has the necessary infrastructure at the language level, though.
FWIW, I'm working on a lightweight, event-driven webserver and general server framework (like twisted or tornado). It will be released under a BSD-style license at the same time as my distributed filesystem (the project driving its development).
