How to remove all login errors on wp-login.php – lostpassword

Solution: 

You can hide the html for error message using css:

<?php function hide_error() { ?>
    <style type="text/css">
       .login #login_error{
           display: none;
       }
    </style>
<?php }
add_action( 'login_enqueue_scripts', 'hide_error' ); ?>