For lua5.2, you need to only use lua:
$ pkg-config --libs lua
-llua -lm

It makes it difficult to write portable Makefiles, since pkg-config --libs lua returns "package not found" on other distributions

upstream does not provide pkg-config files, so it's up to the distro to add them if they want them. How they add them is up to the distro, so you can't count on anything, you need to use conditionals to search for the right one.

I believe Fedora/RH do it the same as Arch and using "lua" should be correct. Debian and it's derivatives are different.

I acknowledge that the approach by arch is correct, but it is not logical to have explicit versions for all, but the current, verison.

A symlink /usr/lib/pkgconfig/lua5.2.pc -> /usr/lib/pkgconfig/lua.pc would automatically be overwritten when 5.2 is no longer the current version, since that would then install a distinct file like 5.1 and earlier versions did when they were replaced.

I'd like to add another perspective to this which was pointed out by a fellow Arch user:
'It makes no sense that one can request pkg-config info on version 5.1 but not 5.2 when they are both installed'

I reckon that the fix to this is trivial (have lua package install a symlink to it's pkgfile with the name of its current version; lua5.2.pc) and without implications (since older lua versions will install their own pkg-config file, overriding the symlink, meaning that when 5.2 is replaced by a new version, a package 5.2 will be created, which will (if it behaves like 5.1) install a pkg-config file named lua5.2.pc thus overriding the symlink).

[Duplicate comment deleted]

The only reason why we have a lua5.1 package is because some software in our repositories still needs it. In the end it will just disappear. Probably there will never be any lua5.2 package.

All changes done to lua5.1 to make it parallel installable with lua is done by Archlinux and is not vanilla in any way. We should not apply this to 5.2.