1. alice@lavaboom.com sends an email to bob@gmail.com
Alice already has a keypair (generated automatically at registration), and Bob has one too. Alice adds Bob as a contact (or does nothing and is matched to Bob's key from a public key server), and sends him an email. The email contents + metadata is encrypted before they leave the Lavaboom email client, and are encrypted all the way to Bob. If Bob uses an email client with PGP support, then he can decrypt the email.
2. alice@lavaboom.com sends and email to zulu@lavaboom.com
Same scenario as above, except that key exchange is done automatically for Lavaboom users (and emails don't leave our servers, making the process even more secure).
3. alice@lavaboom.com sends and email to carla@gmail.com
Carla doesn't use PGP, so Alice's email needs to be sent as plaintext. However, before storing the email to the database, it is encrypted with Alice's key, and the plaintext version (residing in RAM) is deleted as soon as the mailer reports successful delivery. This way, only Alice has access to her data, and Lavaboom is Zero Knowledge in respect to email contents.