Lua is an interpreted/compiled language that its own compilers and isn't usually translated/compiled with a C compiler. What tools should be used to reverse engineer an application written in
If your application is compiled to a binary you might still be able to use normal debuggers like IDA. However, Lua has its own tools for decompiling from machine code and byte code. These links should be kept up to date by the Lua community.
Lua Wiki: LuaTools
If you need support for Lua 5.2 LuaAssemblyTools is the first to support that.