No need. The cached files are saved and managed by LSWS.

On Magento side, you can issue a flush command from the command line either manually or by cron:

magento_dir/shell/litemage_purge.php

Usage:  php litemage_purge.php -- [options]
--products <product IDs>    Comma delimited product IDs
--cats <category_IDs>       Comma delimited category IDs
--stores <store_IDs>        Comma delimited store IDs
--tags <raw tags>           Comma delimited raw tags. You need to understand LiteMage internals to use this.
--all                       Flush all cached files in LiteSpeed Web Server.r.

If you want to delete the physically cached files, you can use lsws/admin/misc/cleanlitemage.sh But it's not really necessary. LSWS will schedule to do it when the server is not busy.