Much as Athanasius suggested in Re: how to save patterns found in array to separate files, you can solve this issue using a hash. In particular, you want to use HASHES OF HASHES (as described in perldsc, see also perlref, perlreftut, perllol). Your first index is probably your filename, and your second is the line content:

use strict;
use warnings;

my %content;
for my $animal ('dog', 'cat') {
    open my $fh, '<', "/tmp/$animal.txt" or die "Couldn't open $animal
+: $!";
    while ( my $line = <$fh> ) {
        ++$content{$animal}{$line};
    }
}

for my $animal ('horse', 'lama', 'camel', 'tiger') {
    open my $fh, '<', "/tmp/$animal.txt" or die "Couldn't open $animal
+: $!";
    while ( my $line = <$fh> ) {
        for my $other ('cat', 'dog') {
            print "$other: $line" if $content{$other}{$line};
        }
    }
}
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