With live chat Business and WebSocket you have the possibility to send emails via PHP Mail() or SMTP. Standard after installation is PHP Mail() which will work fine in 99%, however some clients prefer to send emails via SMTP.
Please go to Settings - Settings and scroll down to the bottom.
The settings for your SMTP Mail Server can be found with your web host, if Mail() has been chosen no more information is necessary.
Important here is that you have to use the Gmail Address for your main email address under settings otherwise Google won't let you send email through their server.
Another hint for Gmail accounts, activate less secure apps: https://www.google.com/settings/security/lesssecureapps and also make sure 2 step authentification is turned off.