Nothing is safe!
There is an option to log you our after the browser is closed and/or in 15 minutes inactivity.They encrypt everything so I believe if they even got into their server there wouldn't be much valuable information anyway.
Used LastPass for years, the only security issue is when you save your password to your PC - could be an issue if someone stole your laptop.
I personally wouldn't trust anyone or any site with my passwords easier to store them on an offline device to stay safe
is it on the cloud or local?