It seems those plugins might not be that well maintained.
There are some tools listed on the LUA users wiki at http://lua-users.org/wiki/DocumentingLuaCode , but at a quick glance none of those tools have been updated any recently.
I looked at how lua generates its reference manual, they use a custom script "our format" inspired by LaTeX to generate HTML/Latex/Docbook. http://lua-users.org/lists/lua-l/2017-12/msg00159.html
At the risk of hijacking this task which is about Doxygen, I am a huge phan of Sphinx which happens to have a plugin to support lua, maybe that can be used instead of Doxygen https://pypi.org/project/sphinx-lua/. Might be worth investigating. It supports two syntax:
- EmmyLua a plugin for IntelliJ that supports Javadoc like comments and is the syntax supported by default by sphinx-lua https://github.com/EmmyLua/IntelliJ-EmmyLua
- Somewhat support ldoc code generator https://stevedonovan.github.io/ldoc/manual/doc.md.html , last code update 4 years ago.