[...] At this point, it seems to me that going the install via the terminal, Apple users have to use sudo make install to things working properly.
That is not strictly true. macOS users can, and often do, change permissions on /usr/local/* to support non-sudo installs. E.g., if you use homebrew, it is assumed by the default configuration that the user has write permission to /usr/local/* -- this can be done with:
sudo chown -R $(whoami) $(brew --prefix)/*
A couple years ago, homebrew assumed that the user has ownership of /usr/local but High Sierra made that difficult (impossible?), so now only the subdirectories of /usr/local are affected.
Why does homebrew prefer this approach? The philosophy seems to be that use of sudo (or logged in as root) is dangerous since you don't know, without reverse engineering, what the makefile or script is going to do. So it is better to install as a normal user who owns /user/local/* -- note that nothing in those directories is used by macOS itself.
So, it is true that after a fresh installation of macOS, the `sudo make install` is the quickest way to install Lua. That said, it is not necessary to use that approach, and many users prefer to take a different approach.