1) June 28th: FBI/DoJ obtains lawful court order for a pen register trace on Snowden's email account. 2) June 28th-July 9th: Lavabit fails to comply. 3) July 9th: Lavabit held in contempt, which is clearly appropriate as they did not respond to a lawful court order. 4) July 9 - August 1: FBI obtains search warrant for Snowden's email. Lavabit challenges warrant on the irrelevant technical grounds that they encrypt all users' email with same key. 5) August 8: Lavabit shuts down, because it turns out that hosting email for the criminal class carries real risks and isn't terribly lucrative.
You can't wave off court orders just because you think the Internet is some kind of libertarian cyber-paradise where mortal laws do not apply. Court orders and search warrants are lawful means of investigation. Lavabit's business was not compatible with US laws or probably the laws of any country more developed than Zimbabwe.