Cloudways does not have an email server. In order to do what you need (having your own email address under your domain), you need to use a forward service which creates email@example.com for you, it then will redirect any emails sent to that address to your gmail inbox. Once connected to your gmail account, you can both send and receive emails under firstname.lastname@example.org.
Here's the guide http://www.custompcguide.net/setup-your-own-domains-email-accounts-for-free-via-mailgun-and-gmailhotmail-for-cloudways-digital-ocean-serverpilot-and-vultr-vps/. Good news is it's free.
You're better off using mailgun. It's free and you can exactly route email@example.com -> firstname.lastname@example.org as you want. Check out this tutorial http://www.custompcguide.net/setup-your-own-domains-email-accounts-for-free-via-mailgun-and-gmailhotmail-for-cloudways-digital-ocean-serverpilot-and-vultr-vps/