The File::Basename documentation says:

dirname() and basename() emulate the behaviours, and quirks, of the shell and C functions of the same name. ... dirname ... This function is provided for compatibility with the Unix shell command dirname(1) and has inherited some of its quirks. In spite of its name it does NOT always return the directory name as you might expect.

Although it doesn't say what exactly those quirks are. To get a directory ../lib relative to the script into @INC using only core modules, I might suggest the following, although there may be some tricky symlink situations where they return different results (abs_path goes out to the filesystem, the second code example does not). Then the question becomes how likely you think that might be. Test cases are best :-)

use FindBin;
use File::Spec::Functions qw/updir catdir/;
use Cwd qw/abs_path/;
use lib abs_path( catdir( $FindBin::RealBin, updir, 'lib' ) );

# - or -

use FindBin;
use File::Spec::Functions qw/splitdir catdir/;
use lib do { my @p = splitdir $FindBin::RealBin;
    catdir @p[0 .. $#p-1], 'lib' };
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