Sounds like they only use 2 datacenters, or maybe even only single primary one with a "backup".
"Update: 1:28 pm ESTSource http://blog.lastpass.com/
Though one of our data centers remains completely down, the service is generally stable and should be available to the majority of users (with the exception of login favicons). Some users may see connection errors but should still be able to access their data. We continue to work as quickly as possible to get the service back to 100%. "
"Aug 12, 2014 - One of LastPass' datacenters has been down since 3:57am EDT. The service is now running fully off one Herndon VA datacenter and we have been engaged with our provider all morning. Currently favicons/sprites are impacted. We are doing what we can to minimize the impact and apologize for the inconvenience. "
For LastPass users that want an offline solution to prevent this type of problem in future consider LastPass Pocket
This is LastPass link specifically about offline access https://helpdesk.lastpass.com/password-manager-basics/your-lastpass-vault/offline-access-to-your-lastpass-vault/