This displays a "directory" post type on the home page, sorted by the meta_key "last_name" in alphabetical order

font_page_directory_query

<?php
/**
 * Load 'directory' post type archive on home page
 * Orderby the meta_key 'last_name' ASC
 *
 * Reference: http://wptheming.com/2014/10/displaying-a-custom-post-type-archive-on-the-front-page/
 */
function prefix_directory_front_page( $query ) {

    // Only filter the main query on the front-end
    if ( is_admin() || ! $query->is_main_query() ) {
    	return;
    }

    global $wp;
    $front = false;

	// If the latest posts are showing on the home page
    if ( ( is_home() && empty( $wp->query_string ) ) ) {
    	$front = true;
    }

	// If a static page is set as the home page
    if ( ( $query->get( 'page_id' ) == get_option( 'page_on_front' ) && get_option( 'page_on_front' ) ) || empty( $wp->query_string ) ) {
    	$front = true;
    }

    if ( $front ) :

        $query->set( 'post_type', 'directory' );
        $query->set( 'page_id', '' );
        $query->set( 'meta_key', 'last_name' );
        $query->set( 'orderby', 'last_name' );
        $query->set( 'order', 'ASC' );

        // Set properties to match an archive
        $query->is_page = 0;
        $query->is_singular = 0;
        $query->is_post_type_archive = 1;
        $query->is_archive = 1;

    endif;

}
add_action( 'pre_get_posts', 'prefix_directory_front_page' );