Google has a option to keep the Two Steps Verification activated and connect your email on external apps, it is a alternative case if you wouldn't like to turn the two steps off.
1. While logged in on your Google account in this link: https://myaccount.google.com/security and with the Two Steps Verification on, go into Security > How you sign in to Google > 2-Step Verification and choose the option "App Passwords".
2. On App passwords area, go into Select app and choose "Other".
3. Then on Select device put your site URL on the field and click on Generate.
4. The generated password will appear on the screen, just copy and paste it on your eDirectory email settings.
5. Connecting the password on your site.
Just remembering Google settings for email configuration:
Server: smtp.gmail.com
Authentication: SSL
Port: 465
Email: Your email account.
Username: Your email account.
Password: The generated password.