I am asking this because Google is already managing password in Google Chrome password manager. Having a dedicated app like LastPass would make everything easier.
Google offers "Smart Lock for Passwords" service in Android. This service is part of the whole android suite on your android device.
Using this, google offers to save passwords for services offered by your apps. This passwords are synced to your google account and are accessible(and auto suggested/filled) on corresponding mobile app, Chrome desktop app or Chrome mobile app. The only catch here is that you cannot see the passwords directly on your mobile phone natively. However, You get a link in Google Services "Smart Lock for Passwords" section to access your passwords, which redirects you to the google account web dashboard portal. After logging in to the above portal you can view and manage your saved passwords.
You can turn this service ON/OFF from "Google Services" option in your Phone Settings.