Lua is quite amenable to being developed with from the command line and doesn't need any specialised tools to get started. But there are a number of IDEs available which may suit developers.
Koneki LDT is an open source Eclipse project which brings the functionality of the Eclipse IDE to Lua. It offers syntax colouring and variable highlighting, error marking, code templates, outlines, folding and formatting, and debugger support. LuaEclipse is an earlier project developed to provide similar facilities but the project appears to have stalled.
Android users will find they can use Lua on their smartphones and tablets as it is one of the supported languages of SL4A, the Scripting Layer for Android.
Another cross-platform plugin which extends a well known IDE is Lua for IntellijIDEA. This Apache 2 licensed library for the community edition of JetBrains IntelliJ has the usual editing features but debugging support is still experimental, as are newer features such as variable refactoring and LuaDoc support.
Lua for Windows is a "batteries included environment" for developing Lua on Windows and comes complete with a SciTE-based Lua IDE, Lua reference manual, examples, compiler and other useful components.
Windows users will also find LuaEdit useful; it offers a project-oriented IDE and debugger, complete with syntax highlighting and auto-completion. Its licensed under the GPL, though its debugging engine has recently been re-licensed under the LGPL.
Another proprietary IDE and debugger for Lua, this time for Windows only, is Decoda. It is notable because of its use by various game developers and other companies.
Some uses or variations on Lua are worth looking at, if only to see the things Lua has enabled. For example, Löve is a open source Lua-based framework for creating 2D games, offering Lua accessible libraries for using audio, graphics, physics, timing and joystick, and a way to package a game and its graphic assets into one file. Worth looking at if you want to get into Lua while making things happen on screen, Löve is available as binary for Windows, Mac OS X and Ubuntu and as source for compiling on other platforms.
Codea is a proprietary application for working with Lua but it takes Lua to a place few languages have been; running on un-jailbroken iPads. Designed as an environment to learn coding and experiment with touch sensors and accelerometers, Codea offers an IDE and simple runtime environment on the iPad, but is still limited in usefulness by Apple's rules about executable code.