Lavabit should not have shutdown because of the actions of Edward Snowden. No company should be closed or shutdown because of the action of one person using the service. Would this question would have been asked if Edward Snowden was using Google Mail instead of Lavabit? No, so it makes no sense to ask it about Lavabit.
No, Lavabit should not have shut down Snowden's email provider, because Snowden exposed an important issue. Americans are very concerned about the issues that Snowden brought to light. With so much public support, one cannot fault Snowden for taking the actions that he did, or the people who want to protect him. Snowden exposed what the government is doing.