The FSSTND states that the /lib directory contains those shared library
images needed to boot the system and run the commands in the root filesystem,
ie. by binaries in /bin and /sbin.

Shared libraries that are only necessary for binaries in /usr (such as any 
X Window binaries) must not be in /lib. Only the shared libraries required
to run binaries in /bin and /sbin may be here. In particular, the library 
libm.so.* may also be placed in /usr/lib if it is not required by anything
in /bin or /sbin.

At least one of each of the following filename patterns are required (they 
may be files, or symbolic links):

libc.so.* The dynamically-linked C library (optional)
ld*       The execution time linker/loader (optional)

If a C preprocessor is installed, /lib/cpp must be a reference to it, for
historical reasons. The usual placement of this binary is /usr/bin/cpp.

The following directories, or symbolic links to directories, must be in 
/lib, if the corresponding subsystem is installed:

modules   Loadable kernel modules (optional)

/lib<qual> : Alternate format essential shared libraries (optional)

There may be one or more variants of the /lib directory on systems which
support more than one binary format requiring separate libraries.

This is commonly used for 64-bit or 32-bit support on systems which support
multiple binary formats, but require libraries of the same name. In this 
case, /lib32 and /lib64 might be the library directories, and /lib a symlink
to one of them.

If one or more of these directories exist, the requirements for their contents
are the same as the normal /lib directory, except that /lib<qual>/cpp is 
not required.

/lib<qual>/cpp is still permitted: this allows the case where /lib and 
/lib<qual> are the same (one is a symbolic link to the other).