I work on a C/C++/Lua server stack, so this is right up my alley. But as a MSVC native I'd have to spend hours trying to decipher your Makefile to port it to Windows before I could even evaluate it.
Use virtualbox, create a small Linux VM, and run it alongside whatever else you've got on your machine. Its simple enough that its sort of a duh - if you were really interested, you could get the VM and bootable Linux dev environment running in less than an hour. I'd be surprised if it took you 20 minutes to look at this stack, build and compile, and learn about it that way...
I've only tried building it on OS X and Linux so far. As far as I know, basically everything but the build process is compatible with Windows. I'll look into it when I get a chance.
Not the OP, and not a Windows user at all (100% Linux, except for OSX buildservers..) but I can answer as an experienced Lua developer the "IDE Question" in two ways, for Lua scope of application, as well as developer-style, is universal:
In a GUI scenario, I use SublimeText for all lua projects and as a cross-platform, 'responsible editor', it provides a nice development enviroment. You can set up buildtools, run them, get output, etc. Generally for my needs it works fabulously. File->Open {directory of main.lua}, then everything works - Global Definitions, Refactoring, etc. Find definitions, see global usage, etc. Code-Completion gradually starts to work more and more, but I don't rely on such 'features' in an IDE. I feel comfortable with little help from an IDE.
In a non-GUI scenario (embedded), I use vim+cscope as my principle IDE. Same idea as ST - open the folder containing main.lua, work from there. Cscope works for Lua, and is also amazing if you do FFI hacking, too .. well generally cscope is my grep, but if I don't have it, of course grep works too ..