Question

The path used by require to search for a Lua loader.

At start-up, Lua initializes this variable with
the value of the environment variable LUA_PATH or
with a default path defined in luaconf.h,
if the environment variable is not defined.
Any ";;" in the value of the environment variable
is replaced by the default path.

A path is a sequence of templates separated by semicolons.
For each template, require will change each interrogation
mark in the template by filename,
which is modname with each dot replaced by a
"directory separator" (such as "/" in Unix);
then it will try to load the resulting file name.
So, for instance, if the Lua path is

 "./?.lua;./?.lc;/usr/local/?/init.lua"

the search for a Lua loader for module foo
will try to load the files
./foo.lua, ./foo.lc, and
/usr/local/foo/init.lua, in that order.