How to auto add nofollow to links in custom field?

This is something you cannot change in the field it self, but in the template file.
Copy and paste here the template file where this option is outputted.

Another way will be to add a javascript snippet to you head, if you have such option in you template.

Comment here and we’ll see what the best solution is.

Update:

I think best solution for you is to use 2 different custom fields – one for the url (call it Links, but put only the url and not the full html link) and one for the link title (call it Links_title, and put just the text you want to be linked).
Then put this code in your template to output it:

    <a href="https://wordpress.stackexchange.com/questions/180450/<?php echo( get_post_meta( $post->ID,"Links", true ) ); ?>" title="https://wordpress.stackexchange.com/questions/180450/<?php echo( get_post_meta( $post->ID,"Links_title", true ) ); ?>" rel="nofollow">
     <?php echo( get_post_meta( $post->ID, "Links_title", true ) ); ?>
     </a>