LastPass is safe to use. This is the one place that you use one really long password or passphrase which is better IMO.
How does LastPass work? All of the decryption takes place on your local machine and not on their servers. All of your data is encrypted, hashed, and salted meaning if someone were to hack them, they would not be able to just grab your information without first having your password. Your password could still be brute forced if it were weak. You can also use dual authentication using a phone app for LastPass.
Simply put, I would not use them if I did not think it were safe to do so. All of the decryption work is done on your computer and no their servers. That says a lot about their service right there.