Gmail recently changed its policy. Now it does not permit anymore to use the Gmail SMTP server to send email on behalf of another domain. This is to avoid spammers and enforce some security policy.
So, if you have an address firstname.lastname@example.org you also must have an SMTP server for bbb.com (e.g. smtp.bbb.com) and an account on that SMTP server. If you have those, you can enter that information in Gmail and set up that account as an alias.
Essentially, Gmail becomes just a client for that address, using the address’ SMTP server instead of Gmail SMTP server, to send mail for that address.
You can continue to use the Gmail SMTP server to send mail only for other Gmail addresses, or for Google Apps addresses.
The method described below in http://webapps.stackexchange.com/a/72975/60630 works for sending mail, but has a drawback: your mail is not verified and risks going to the SPAM. This is because Gmail uses SPF and DKIM. You could add google in your domain's SPF, but not authenticate with DKIM.