Because of how ECC works, only someone with the second “private” key can decipher messages encrypted with the public key. To protect the private key from attackers, it is encrypted using the Advanced Encryption Standard (AES) with a 256 bit key. AES is a synchronous encryption scheme that uses a secret passphrase to encrypt/decrypt a ciphered message. In the case of Lavabit’s secure e-mail system, the ciphered message is a user’s private key and the secret passphrase is a hashed version of the user’s password.
In other words, in order to decrypt past emails, the account password must be known (or brute-forced, and Lavabit's system does not seem particularly robust against brute-force attacks).
Now, we know Lavabit has received sealed court orders requiring the disclosure of their SSL private key. There may be even more repressive sealed orders, or NSLs, that require him to cooperate in their collection.
One key problem is that even though Lavabit could have provided instructions and encrypted email downloads that would enable prior users to securely download their email archives and decrypt them on their own computers, he chose to enable the recovery only upon production to the server of the account password necessary to decrypt past emails.
Even worse, SSL Labs shows that this new site does not support perfect forward secrecy, while the old one did. No PFS means when FBI/NSA are provided with the new key (just as they were with the old one), they can decrypt all prior sessions--and see all the passwords that were entered for 'recovery'.