Need edit profile link in the menu for logged in users

You can get the current user’s info by using wp_get_current_user() and then get the profile edit link by using the user's ID as following:

 function wpse_125929_login_logout( $items ) {
    if ( is_user_logged_in() ) {
        $current_user = wp_get_current_user();
        $profile_edit_url = admin_url( 'user-edit.php?user_id=' . $current_user->ID );
        $profile_link = '<li><a href="' . $profile_edit_url . '">Edit Profile</a></li>';
        $logout_url="<li><a href="". wp_logout_url() .'">Logout</a></li>';
        $items = $items. $profile_link. $logout_url;   
    } else {
        $login_link = '<li><a href="'. site_url('wp-login.php') .'">Log In</a></li>';
        $items = $items. $login_link;
    }  
    return $items;
}
add_filter( 'wp_nav_menu_items', 'wpse_125929_login_logout' );