The installer(s) may provide execution of *.lua with a shell.open.command.
E.g.:
[HKEY_CLASSES_ROOT\Lua.Script\Shell\Open\Command]
@="\"C:\\Program Files (x86)\\WinLua\\Lua\\5.3\\bin\\lua.exe\" \"%1\" %*"
The last %* is essential to allow Lua-Script to recieve command arguments.