Fortunately they don't have access to your unencrypted passwords.. https://lastpass.com/support.php?cmd=showfaq&id=1096
This is important because your sensitive data is always encrypted and decrypted locally on your computer before being synchronized. Your master password never leaves your computer and your key never leaves your computer. No one at LastPass (or anywhere else) can decrypt your data without you giving up your password (we will never ask you for it). Your key is created by taking a SHA-256 hash of your password. When you login, we make a hash of your username concatenated with your password, and that hash is what's sent to verify if you can download your encrypted data."