As it turns out, it’s possible with Lua going back to 5.1 to not allow undeclared global variables:

https://www.lua.org/pil/14.2.html

That code looks like this in Lua 5.1:

  function set(name, val)
    rawset(_G, name, val or false)
  end
  function exists(name)
    if rawget(_G, name) then return true end
    return false
  end
  throwError = {__newindex = function(self,name) error("Unknown global " .. name) end,
                __index = function(self,name) error("Unknown global " .. name) end
  }
  setmetatable(_G,throwError)

Then, to use

  set("a") -- set"a" also works
  a = 1