I right clicked the project, went to configuration properties->Linker->Input and set Additional Dependencies to lua5.1.lib and lua51.lib.
Then I went to Linker->General and set Additional Library Directories to C:\lua
And did the same for C/C++->General->Additional Library Directories
The header files are including fine it seems.
Can you try and compile this and tell me your settings?
Edit
I think I've found the solution, alot of people on the web have issues with compiling the lua libs in C and their modules in C++. Turns out you need a lua5.1.lib and dll compiled as C++ if you plan to use it with C++ compiled libraries, I will try this now.
Edit
Turns out all I had to do was recompile it from source, not sure why that worked. If that still doesn't work for you, compile it in C++ by changing all the .c files to .cpp files.
error loading module 'luatestdll' from file 'C:\Program Files\LOVE\luatestdll.dll':
The specified procedure could not be found.
stack traceback:
[C]: ?
[C]: in function 'require'
[string "main.lua"]:1: in main chunk
How can I verify the names got exported correctly?