Ummm yeah...lastpass doesnt store your passwords on their site, they are stored locally on your computer. Yes lastpass was broken into however the only info they got was user names and passwords for the site. They did not get any other info as I said your passwords are not stored on the actual site, but locally in your computer.
They store passwords encrypted by your master passphrase on their servers. Thats why you can install lastpass on any computer, and, after entering your email and passphrase, get access to all your stored passwords. If it all works as they say - your local lastpass connects to lastpass servers, downloads your data in encrypted form, and decrypts it locally.