I too am having problems compiling.

When debugging it gives me the errors: cannot open source file "lua5.1/lua.h" in file LuaCompat.h ,

lauxlib.h and lualib.h also cannot be opened.

What compiler and IDE (if you are using one) are you using?

Sorry, Visual Studio 2015, what is the IDE?

That is the ide, the compiler is Microsoft visual c, but that's all I need. Did you set up the solution manually or did you download the premade one?

Manually, from the Powder Toy github repository, using the premade project gives me even more errors, like the whole src folder was missing.

Check your project properties under VC++ directories > include directories. Check that you added the $(ProjectDir)\includes\lua5.1 setting 

Sorry I can't help any better, I don't feel like turning on my computer at 1am.

Edit: I'm going to sleep now, if no one has helped you by the morning, I can do it but right now i can only assume that you got caught up with something in real life. 

Yeah, still getting the same error. I had $(ProjectDir)\includes\lua5.2 instead, but changing it to 5.1 didn't seem to help.

And only now i noticed the meaning of that setting, $(ProjectDir)\data or $(ProjectDir)\src lead to the folders with these names in the directory, but i dont have any folder named "include".

I got the updated premade project and built mostly without errors, but in the end I get an error about CreateFile2 in KERNEL32.dll.

Is that the only error you get? And can you copy and paste the complete error, (if it is very large, put it on pastebin and share the link here)?