I've made a personal Live CD on Ubuntu builder but I didn't add a password to the Live CD.
Is it possible to add a password to a live CD in any way? (before or after creating the CD)
You will have to edit the casper scripts.
This varies slightly between versions of Ubuntu, see:
https://help.ubuntu.com/community/LiveCDCustomization#Removing_the_.28Casper.29_Autologin
As Ubuntu wiki page says:
You can set a password during a LiveCD session by opening a terminal, and typing in:
sudo passwd ubuntu
Note that this will set the password only for the current session (which is far less useful).