Noindex Posts From Certain Authors In WordPress

From codex: is_author() is a conditional tag which determines whether the query is for an existing author archive page.
so it does not work for your scope.

Best solution, instead of using the template file header.php is to write a function in functions.php hooking the proper action wp_head:

add_action('wp_head','AS_exclude_author_from_indexing');

function AS_exclude_author_from_indexing(){
  $toIndex = array(111,112,113);
  $user_id = get_the_author_meta( 'ID' );
  if( !in_array($user_id,$toIndex)){
    echo "<meta name=\"robots\" content=\"noindex,follow\">".PHP_EOL;
  } 
}