I'm having the exact same problem. I have also followed all the steps in the recommended FAQ. I've downloaded and reinstalled Lastpass. I've disabled or uninstalled all extension. I've cleared cookies. I've cleared local cache. If done a cold reboot. Nothing seems to work.
Still I get this same warning message: 'An error occurred while attempting to contact the server. Please check your internet connection.'
I believe the problem is that the local Lastpass can't reach the server. So we can use the passwords we have saved because they are stored locally. However, we can't create new ones, and we keep getting the error message whenever Lastpass tries to contact the server. Can someone from Lastpass verify, and can something be done about this?