This is something we could automatically do in the future.
In the meantime the cron job workaround proposed by DirectAdmin could work on Enhance with a little modification. The differences being that the path to your websites would be /var/www/*/public_html and the command to restart openlitespeed would be:
docker exec -it openlitespeed /usr/local/lsws/bin/lswsctrl restart
Also you won't have access to the cgid binary they're using to detect the start time as that's within the openlitespeed container. You would have to use
mmin and pick a time which is slightly less frequent than your cron job.