Actually, I don't think so, if he was a paying user. Everything on-disk was encrypted for paying users, and since lavabit had to shut down completely to not "be complicit in a crime against the American public", I assume that the NSL wanted them to make a change like Hushmail did in the past, to send the user's password to the server on the next login so that they can decrypt all emails.

I would assume that the NSA had already forcibly installed something that would compromise all further access to lavabit mail. Therefore the only option that doesn't reveal data is immediate shutdown.

That's not how Lavabit worked.