Well as for simply supporting Lua in browsers, aside from the obvious Emscripten/ASM.js way, which would work for practically all browsers which support JavaScript, Lua can run as a PNaCl app in Chrome/Chromium, see: https://chrome.google.com/webstore/detail/lua/nkcnhkobblkmia...

Of course this is only a proof-of-concept which just runs a Lua REPL in the browser. I wonder if it is possible (and if so, how hard it is) to make the browser run <script language="lua"></script> code.