@Sushantfitness I will make an assumption that you used the certonly command to initially create the cert. Let me know if that is not the case.
One way is to use the --deploy-hook option on the renew command. The hook command runs after a renewal that successfully creates a new cert. You set the command to restart litespeed or whatever else you need. And, if you have not already, setup a cron to run the renew. So, something like:
certbot renew --deploy-hook "command to reload/restart litespeed"
You could also add the deploy hook in a certonly command and it will save the value in the renewal conf. That avoids needing to use it with the renew command.