Day One on iOS has the option to enable a passcode or use Touch ID to unlock the whole app. The app-locking passcode should not be confused with the account password.
Tap Settings > Passcode & Touch ID to get started
Enable Passcode
Create a new 4-digit passcode
Now you will see the customizable options for Passcode and Biometrics. The options are:
Require After… which allows you to set when the passcode will be required
Touch ID – If your device has Touch ID enabled and you have a fingerprint registered you can use this option to unlock your journal
Face ID – if your device has Face ID enabled you can use this option to unlock your journal
Prompt for Touch ID/Face ID on Startup – as soon as you open Day One, the Touch ID/Face ID prompt will appear.
FAQ
How do I reset my passcode?
Can I set a passcode for individual entries or specific Journals?
The passcode will only lock the whole app. It is not possible to lock individual entries with a passcode or use a passcode for just one Journal.