You have the user id# that uniquely identifies the user. So prepend the user id value to the list name the user chooses, to save the list value. For example, if user #1234 creates a list called xmas, then do
$args = wp_insert_term ('1234_xmas', 'list');
Next add a custom field to the user. And store ‘xmas’ into that field.
See: http://justintadlock.com/archives/2009/09/10/adding-and-using-custom-user-profile-fields