How to enable password lock on Notes in iOS 9.3?
The relatively difficult-to-find solution to the problem is to go to the Note you wish to lock:


in the top-right corner, tap the "Share" icon
on the bottom row, there will be a lock symbol with a caption that says "Lock Note". 
select that symbol
you will be prompted to create a password that locks this note, but remember that this single password will secure all your protected notes, not just the note you're on. 


You can also use Touch ID to secure your notes. Remember that if you secure the note, it will no longer be accessible by devices running versions of OS X older than 10.11.4, or devices running a version of iOS different from 9.3 or higher. Next time you try to open that Note (or others that are locked with the passcode), you'll be prompted for your password to unlock it.

You can change the Notes password by going to your Home screen, then Settings > Notes > Password.