Lua comes with debugger interface, so that users can write their own monitoring code (e.g., for a debugger, tracer, or profiler) through the Lua Debug library [1]. Some examples are below.
Decoda is Graphical debugger with remote debugging support[Decoda] (Debugging does not work "from the box")
[GRLD] - graphical remote lua debugger with source code, free of charge for non-commercial use. Works with lua-jit too. (Does not work "from the box". Very buggy.)
[akdebugger] Debugger and editor for Lua. Plugin for Eclipse.