The best way to protect all of your passwords is by using a two-step Verification.
First step: entering your password; Second step: your verification tool.
With both solutions you have a master password, which you use to login and view all of your passwords.
Now, what about the two-step Verification?
When using a two-step Verification tool with Lastpass you can choose between Google Authenticator app, Lastpass Authentificator app and others. You can even use these apps if your phone is offline.
You also have the versatile YubiKey as a two-step verification tool, which does not require software installation or a battery; just plug it into a USB port, and touch the button for secure and strong authentication. A YubiKey is something you have that provides security protection beyond something you know (like a username/password). Even if someone steals your username and password (which is happening in bunches lately) they can’t get into your account without your physical key.
Yubikey is made by Yubico, more information here: https://www.yubico.com/why-yubico/for-individuals/