Create a php file with content like in root folder web
<?php
require( './wp-load.php' );
if (class_exists('\LiteSpeed\Purge')) {
do_action('litespeed_purge_all');
echo "Litespeed flush cache successfuly.";
}
save it with name like purge.php
then curl it with cron job e.g.
curl -I -XGET https://domain.com/purge.php