One scenario is that you already have big C/C++/Java/C# (etc) applications and wish to let your users script those applications. Lua will only add about 150-170K, which gets you a modern extension language which understands your special needs (like sand boxing) and can be easily integrated with your code.
The other is that you have a lot of components which you use in your work flow and you are looking for a glue language to easily bind them together quickly without messy recompilation. (See Ousterhout's Dichotomy.)
Another powerful use case which combines these two is embedding Lua as a aid to debugging. It is possible to provide an intelligent debug console (even for GUI applications, such as Java/Swing) running Lua, which can let you operate inside an application, querying state and running little test scripts.