Using perl, grep on the lines in the file not the filename. For example (using test data instead of your command output)

#!/usr/bin/perl
use warnings;
use strict;

my $awsLists = '/ansible/awsLists';
my @awsLists = ();
if (-e $awsLists){
  open my $fh,'<',$awsLists or die "$!";
  @awsLists = <$fh>;
  close $fh;
}

my $cmd = 'aws ec2 describe-instances --filters "Name=instance-state-n
+ame,Values=running" | grep PrivateDnsNam$';
my @output = <DATA>;#qx/$cmd/;

open my $fh,'>>',$awsLists or die "$!";
foreach my $line (@output){
  chomp($line);
  if (grep /$line/, @awsLists ){
    print "$line found\n";
  } else {
    print "$line not found - added\n";
    print $fh $line."\n";
  }
}
close $fh;

__DATA__
test 1
test 89
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