icloud – Unable to unlock my Mac unless I am connect to internet

So when I want to log into a session, I need to actually be connected to internet, else I am left locked out. It’s been happening for months. I tried resetting the password but no luck, I still need to be connected to log in.

It’s as if the Operating System needs to check the password I enter with the one stored online (iCloud I suppose).

Note that I run macOS Mojave. It’s a MacBook Air of 2013.