I will put dollars to donuts they were after Snowden's contact list. They want to know about his deadman's switch, who holds the keys, and who they have to squeeze to defuse that particular landline.
They're not asking for any particular information that lavabit has now. If they were, shutting down wouldn't be a solution to not handing it over. They are asking for additional access going forward.
I know, but I don't think it's unreasonable to expect that Snowden may be in contact with people that his pursuers are not yet aware of. Tapping his communications would give them a much larger attack surface.
But that additional access would probably include various keys that would let them decrypt previous communication. Maybe the order was to log passwords on login, or something like that, that would allow recovery of the key and decryption of stored data, which may not be possible depending on the original architecture of the system.
