Lavabit was vulnerable to three attackers:
1) The server operator could choose to obtain access to plaintext.
2) An attacker who compromised the server could get access to plaintext.
3) Anyone capable of intercepting the SSL communication could get access to plaintext.
Incidentally, those are the exact same points of vulnerability for a normal (unencrypted) mail service.
One interesting question is why the US government requested Lavabit's SSL key rather than just getting a CA to sign their own. My assumption is because they were interested in past communication that might have already been deleted (perhaps by Snowden). We now know that the US government often logs and stores ciphertext, and we know that Lavabit was not selecting PFS SSL cipher suites.
So when Ladar did eventually provide the SSL key to the government, it's likely that the government was able to use that to decrypt all previously stored traffic and obtain the entire history of transmitted email.
So it's quite likely that Snowden (and all other Lavabit users) did have their email read by the government.