While there are of course similarities between Erlang and Lua and you can use them to write the same types of applications they do have very different targets. Erlang was designed for large scale, massively concurrent, fault-tolerant systems that should never got down [1], which is not what Lua was designed for. So while you will find libraries that do the same thing in both languages it is probably not realistic to expect to be able to write Erlang type applications in Lua. I don't see this as a Lua deficiency, it is just a result of what the languages target.
That being said there are some unexpected similarities. For example while Lua is often described as a scripting language the way Erlang and Lua handle code is quite similar. Both compile code and allow code to be dynamically loaded without having to "relink" the whole system, though Erlang must do this in a concurrent environment. Both languages tend to be used in multi-lingual systems. I know of companies which use them together, Erlang as a form of concurrent, logical "glue" and business logic in Lua, plus other stuff in other languages. Most large systems are diverse so I personally think expecting to find one language which fits everything is unrealistic.
Robert
[1] Got the main buzzwords there.
From: "Jayanth Acharya" <jayachar88@gmail.com>
To: "Lua mailing list" <lua-l@lists.lua.org>
Sent: Wednesday, 18 September, 2013 11:29:08 AM
Subject: Re: Why Lua is not more popular