sol is a C++ library binding to Lua. It currently supports all Lua versions 5.1+ (LuaJIT 2.x included). sol aims to be easy to use and easy to add to a project. The library is header-only for easy integration with projects.
Find it here. A run-through kind of tutorial is here! The API documentation goes over most cases (particularly, the "api/usertype" and "api/proxy" and "api/function" sections) that should still get you off your feet and going, and there's an examples directory here as well.
#include <sol/sol.hpp>
#include <cassert>
int main() {
sol::state lua;
int x = 0;
lua.set_function("beep", [&x]{ ++x; });
lua.script("beep()");
assert(x == 1);
}