This is what I saw in Digital Ocean. They provide 'Load Balancers'. They claim they provide 'Lets Encrypt' SSL for free. They also auto-renew it. Do I need to pay additional amount for that (load balancers)?
Is it like Cloudflare? That they auto-manage Lets Encrypt SSL certificate?
Hosting companies are allowed and even encouraged to do this. While Let's Encrypt does not prefer the hosting companies to add an additional charge for customers who use hosting provider-obtained certificates, it's not forbidden by Let's Encrypt's terms of service, and the question of whether there is any extra charge is between the hosting provider and the customer.
From what you've shown above, it looks like it's free of charge (since it specifically says "free"!) and also looks like it's automated.