Last Pass is very safe. Used for years by many experts.
Their Privacy Statement guards you very well (so you have advantage in court if something happens to any of your passwords/data):
We don't allow you to send LastPass critically important information like your usernames, passwords, account notes, and LastPass master password; instead your LastPass master password is used locally to encrypt the important data that's sent to us so that no one, including LastPass employees ever can access it.
We don't ask you for personal information unless we truly need it.
We don't share your personal information with anyone except to comply with the law, develop our products, or protect our rights.
We don't store personal information on our servers unless required for the on-going operation of one of our services. (For example: If you choose to store login history, we keep login history, if you choose not to, we don't)
Noted here:
https://lastpass.com/aboutus_privacy.php