How to debug LUA

It's kind of hard to say, being that you don't provide any details of the kind of problems you're trying to debug. I assume you're logging any and all errors, because Lua does a pretty good job in that department. That pretty much takes care of compile-time debugging. As for run-time debugging, it depends entirely on the language and environment you're using, but the most obvious thing to do is bind a bunch of functions which use your language's/environment's inbuilt debugging tools and then you can use them from Lua. So have a function which logs to the debug console, and bind that to Lua. Have a function which breaks program execution with the debugger, and bind that to Lua.

To suggest anything else, I'd have to know what kind of issues/problems you're trying to debug.