Add Last-Modified HTTP header in Wordpress

function.php

/**
 * Set the Last-Modified header for visitors on the front-page 
 * based on when a post was last modified.
 */

add_action( 'template_redirect', function() use ( &$wp )
{
    // Only visitors (not logged in)
    if( is_user_logged_in() )
        return;

    // Target front-page
    if( ! is_front_page() )
        return;

    // Don't add it if there's e.g. 404 error (similar as the error check for feeds)
    if( ! empty( $wp->query_vars['error'] ) )
        return;

    // Don't override the last-modified header if it's already set
    $headers = headers_list();
    if( ! empty( $headers['last-modified'] ) )  
        return;

    // Get last modified post
    $last_modified = mysql2date( 'D, d M Y H:i:s', get_lastpostmodified( 'GMT' ), false );

    // Add last modified header
    if( $last_modified && ! headers_sent() )
        header( "Last-Modified: " . $last_modified . ' GMT' );

}, 1 );

/* add last-modified HTTP header to blog posts */
add_action('template_redirect', 'theme_add_last_modified_header');
function theme_add_last_modified_header($headers) {
    global $post;
    if(isset($post) && isset($post->post_modified)){
        $post_mod_date=date("D, d M Y H:i:s",strtotime($post->post_modified));
        header('Last-Modified: '.$post_mod_date.' GMT');
     }
}