This function adds a logo as a first menu item.

functions.php

<?php

function ict_bz_add_logo_to_menu( $items, $args, $logo_path = 'https://placekitten.com/g/150/150', $menu_locations = array( 'primary' ) ) {

	if ( in_array( $args->theme_location, $menu_locations ) ) {

		$logo_item = sprintf( 
			'<li class="menu_item menu_item_custom menu_item_logo"><a href="%s"><img src="%s"></a></li>',
			get_home_url(),
			$logo_path
		 );

		$items = $logo_item . $items;
	}

	return $items;
}
add_filter( 'wp_nav_menu_items', 'ict_bz_add_logo_to_menu', 10, 2 );