Day One on iOS has the option to enable a passcode or use Touch ID to unlock the app.
Tap Settings > Passcode & Touch ID to get started
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.