How to setup email with AWS Lightsail
I would suggest not hosting your client's email through your Lightsail server. There are a lot of extra headaches to consider and there are other services that are more reliable and offer a better more robust user interface than the options available on server.
To get your client a custom domainname email address (ie joe@domainname.com) here are two options:
Zoho - Cost: FREE
You can sign up here: https://www.zoho.com/workplace/pricing.html?src=zmailYou need to verify the domain name for this to work (either by adding an HTML file to the site or a CNAME to the domain)
GSuite by Google - Cost: $5/user/month
You can sign up here: https://inbox.google.com/u/0/search/google%20suite#m_-1052842142248281614_You can also get some good promotional codes to get 20% off the first year - here's one: 9746YLRVNWERPAH
And, to your question about making sure forgot password emails are sent, make sure sendmail is installed on the server (apt-get install sendmail), that the /etc/hosts file contains the following
- 127.0.0.1 localhost localhost.localdomain yourhostnamehere
and that port 25 is open on the server.